Differential Geometry Forum

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.

Threads

Graduate How to show that a locally diffeomorphic mapping from R to R is open?

  • Relative0
  • · Replies 3 ·
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Graduate Tensor: Definition, Examples & n,m Meaning

  • subsonicman
  • · Replies 2 ·
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2

Graduate Transformation of Vectors Confusion

  • Opus_723
  • · Replies 1 ·
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1

Graduate Divergence of tensor times vector

  • Runner 1
  • · Replies 5 ·
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5
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9

Graduate Do Manifolds have distance relations between points?

  • me1pg
  • · Replies 7 ·
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7

Graduate Can unquantized fields be considered smooth curved abstract manifolds?

  • Spinnor
  • · Replies 4 ·
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4

Graduate What is the area of intersection between two adjacent spherical caps?

  • morjo
  • · Replies 2 ·
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2

Graduate Where can I find information on S^3?

  • RicciFlow
  • · Replies 4 ·
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4

Graduate Question about Christoffel symbol's value

  • raopeng
  • · Replies 2 ·
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2

Graduate Orthonormal basis vectors for polar coordinate system

  • V0ODO0CH1LD
  • · Replies 9 ·
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9

Graduate Divergence of product of tensor and vector

  • praban
  • · Replies 18 ·
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18

Graduate Is the Spin Connection Problem Affecting My Derivation of the Dirac Equation?

  • pleasehelpmeno
  • · Replies 8 ·
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8

Graduate Silly question about the Theorema Egregium

  • quasar987
  • · Replies 8 ·
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8

Undergrad Geometry Problem involving packing Hexagons into Circles

  • chriscots
  • · Replies 1 ·
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1

Graduate No metric on S^2 having curvature bounded above or below by 0

  • Relative0
  • · Replies 9 ·
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9

Joko's question at Yahoo Answers (r(t) perpendicular to r'(t))

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Contracting Tensors: Multiply by g^αρgασ?

  • pleasehelpmeno
  • · Replies 3 ·
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3

Graduate Vectors in curvilinear coordinate systems

  • ShayanJ
  • · Replies 12 ·
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12

Graduate What Is the Maximum Value of x for Points on a Plane and Sphere in 3D Geometry?

  • jingu
  • · Replies 11 ·
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11

Graduate Can the Relationship Between Levi-Civita Tensor and Kronecker Symbol Be Proven?

  • raopeng
  • · Replies 2 ·
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2

Graduate How Do You Calculate g(W,W) Using the Given Metric?

  • MathematicalPhysicist
  • · Replies 3 ·
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3

Undergrad What Type of Curve Uses Sequential Control Points from A0 to A6?

  • mymachine
  • · Replies 2 ·
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2

Graduate What Does Locally Euclidean Mean in the Context of Manifolds?

  • friend
  • · Replies 25 ·
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25

Graduate Can a 4-Sphere Have a Circumference?

  • liometopum
  • · Replies 3 ·
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3

Graduate How can a cubic Bezier curve be constructed to have a tangent to a circle?

  • mymachine
  • · Replies 2 ·
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2

Graduate Continuity of the Bezier Curve, Question

  • mymachine
  • · Replies 2 ·
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2

Graduate What Defines the Components of a 2-form?

  • center o bass
  • · Replies 2 ·
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2

Wizard1's question at Yahoo Answers (Isometry)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Can You Recall the Formula for Finding the Area of a Spherical Patch?

  • Curl
  • · Replies 3 ·
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3

Graduate Why Must the Image of U Be Open in \(\mathbf{R}^n\)?

  • dEdt
  • · Replies 6 ·
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6

Undergrad How can I find the angle of a curve in a shape with a given length and radius?

  • uperkurk
  • · Replies 4 ·
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4

Undergrad Laws of area and conservation of momentum

  • almo
  • · Replies 3 ·
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3

Bebe's question at Yahoo Answers (Curv. and torsion)

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate How is the Chain Rule Applied in Geometric Tangent Vectors?

  • BrainHurts
  • · Replies 1 ·
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1

Graduate Using Tensor Notations and Levi Civita Symbol to Prove Lagrange's Identity

  • advphys
  • · Replies 4 ·
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4

Graduate Need Help with Mathematical Proof? - Introducing Myself & Seeking Assistance

  • advphys
  • · Replies 3 ·
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3

Graduate Curl of Gradient: When is a Conservative Field Not Irrotational?

  • TrickyDicky
  • · Replies 28 ·
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28

Undergrad Formulation of the Complex Plane

  • IxRxPhysicist
  • · Replies 3 ·
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3

Graduate Properties of Differentials, Smooth Manifolds.

  • BrainHurts
  • · Replies 1 ·
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1

Graduate Is It More Precise to Define Manifolds as Topological Vector Spaces?

  • TrickyDicky
  • · Replies 42 ·
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Graduate Derivative of a curve traversed in the opposite direction

  • Kreizhn
  • · Replies 2 ·
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2

Mr.Ask's question at Yahoo Answers (curvature)

  • Fernando Revilla
  • · Replies 1 ·
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1

Fascinating Properties: Excluding 998 from 0.001002003004...

  • Jameson
  • · Replies 5 ·
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5

Graduate Understanding Manifolds and Riemann Manifolds: Applications and Explanation

  • umerfarooque
  • · Replies 8 ·
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8

Graduate What is an "induced map"? Is it a Quotient Map?

  • dumbQuestion
  • · Replies 4 ·
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4

Graduate Can a Set of Sections Globally Generate a Vector Bundle?

  • math6
  • · Replies 7 ·
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Graduate Sphere is the object that has the minimal area for a fix volume, proof

  • andonrangelov
  • · Replies 3 ·
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3

Henry's question at Yahoo Answers concerning a surface of revolution

  • MarkFL
  • · Replies 2 ·
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2

Graduate Integral of mean curvature function

  • neelakash
  • · Replies 3 ·
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Graduate Elementary Differential Forms Question

  • mindarson
  • · Replies 5 ·
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Graduate Question about Differential Forms as Size of Projections

  • mindarson
  • · Replies 2 ·
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2

Graduate Equivariant Homotopy: M & N Manifolds, G-Action & Cohomology Rings

  • Kreizhn
  • · Replies 4 ·
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4

Graduate Comparing Norms & Metrics: Axioms & Differences

  • Bachelier
  • · Replies 8 ·
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8

Graduate Divergence theorem question on hyperplanes

  • WannabeNewton
  • · Replies 1 ·
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1

Graduate A rather difficult problem: deltoid inscribed into an ellipse

  • lemma28
  • · Replies 1 ·
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1

Graduate Can Intersecting Planes Be Represented by a New Form of 3D Angles?

  • fromage
  • · Replies 4 ·
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4

Graduate Differentisl geometry internal contraction

  • pleasehelpmeno
  • · Replies 1 ·
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1

David's question at Yahoo Answers (horizontal tangente plane).

  • Fernando Revilla
  • · Replies 2 ·
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2

Graduate Bochner-Weitzenbock formula (-> Laplacian)

  • Sajet
  • · Replies 3 ·
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3

Graduate Diffeomorphisms, Differential Structure, ETC.

  • friend
  • · Replies 17 ·
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17

Graduate Unit of Four Dimensional Space Measurement?

  • Joshuame13
  • · Replies 3 ·
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3

High School What are the key differences between Euclidean and plane geometry?

  • yungman
  • · Replies 8 ·
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8

Undergrad Exploring the Role of Spherical Unit Vectors in Coordinate Systems

  • Opus_723
  • · Replies 7 ·
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7

Graduate Proof by Induction: Closure of Union = Union of Closures

  • Bachelier
  • · Replies 4 ·
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4

Undergrad Equation of an ellipse and tangents

  • Kartik.
  • · Replies 1 ·
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1

Graduate How Can the Laplacian Relate to Einstein Manifolds?

  • Messenger
  • · Replies 9 ·
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9

Graduate Is a cone the degenerate of a 4 dimensional hyperbola?

  • JonDrew
  • · Replies 2 ·
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2

Graduate How to understand differential geometry

  • phyky
  • · Replies 5 ·
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5

Graduate Definition of the boundary map for chain complexes

  • Tac-Tics
  • · Replies 4 ·
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4

Reciprocal Vectors: Representing $\mathbf{u}_i$ in Indicial Notation

  • Dustinsfl
  • · Replies 6 ·
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6

Vector equation of a spherical surface

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate Summing the Mountains and Valleys of a Regular Polygon

  • redount2k9
  • · Replies 4 ·
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4

Graduate The Relation between Cup Product and Wedge Product

  • lavinia
  • · Replies 3 ·
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3

Graduate Can a Triangle Have Angles Over 180 Degrees Without 3D Embedding?

  • Pjpic
  • · Replies 4 ·
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4

Graduate Generalizing Cross Products: Finding Orthogonal Vectors in n-Dimensional Space?

  • rvadd
  • · Replies 5 ·
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5

Graduate How does the curl equation measure rotation?

  • autodidude
  • · Replies 5 ·
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5

Graduate How to find angle after two rotations

  • 1MileCrash
  • · Replies 2 ·
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2

Graduate Does a 3D Half-Edge Data Structure Exist?

  • Ole Lindberg
  • · Replies 1 ·
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1

Undergrad Can you triangulate a triangle? (also, odd sided polygons to represent surfaces)

  • iLoveTopology
  • · Replies 5 ·
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5

High School How to calculate/find the volume of drinking bottles and product containers?

  • kweba
  • · Replies 3 ·
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3

Graduate How to find an angle in spherical geometry.

  • yungman
  • · Replies 3 ·
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3

Graduate Where Does the Coordinate Basis Approach to Lie Groups Break Down?

  • Kontilera
  • · Replies 12 ·
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12

Graduate How to calculate the solid angle of a cone with cone axis arbitrary?

  • soljiang
  • · Replies 5 ·
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5

Graduate Fixed Point Theorem: Unit Square Injection to Bigger Square

  • sammycaps
  • · Replies 12 ·
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12

Position of Particle in a Circular Path: Solution

  • Dustinsfl
  • · Replies 6 ·
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6

Undergrad Surface Constant: What Does It Mean & Impact on Gradient?

  • Summer2442
  • · Replies 10 ·
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10

Undergrad What is a Tensor? Explanations & Understanding

  • VivaLaFisica
  • · Replies 9 ·
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9

Undergrad Determining Areas of Triangles in Hexagon ABCDEF

  • Numeriprimi
  • · Replies 4 ·
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4

Graduate Differential geometry vs differential topology

  • sabw1992
  • · Replies 2 ·
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2

Graduate Definition of the wedge product on the exterior algebra of a vector space

  • phibonacci
  • · Replies 3 ·
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3

Graduate FKG Inequality: Reference & Explanation

  • hedipaldi
  • · Replies 2 ·
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2

Graduate Atlas of complex projective 3-space ##\mathbb{C}P^3##

  • kloptok
  • · Replies 1 ·
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1

Graduate Graphing Covariant Spherical Coordinates

  • jstrunk
  • · Replies 4 ·
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4

Graduate Does Every Circle Bundle Originate from a 2-Plane Bundle?

  • lavinia
  • · Replies 3 ·
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3

High School How Do You Calculate (X,Y) Coordinates on a Circle with a Given Radius?

  • 777funk
  • · Replies 2 ·
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2

Undergrad Where Do Points Sum to Two-Thirds the Perimeter of a Rectangle?

  • Numeriprimi
  • · Replies 4 ·
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4

Graduate Why do different dimensions have different numbers of differential structures?

  • saminator910
  • · Replies 2 ·
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2

Graduate Continuous R^2xR^2xR^2/E^+(2) -> R^3 injection

  • pmsrw3
  • · Replies 1 ·
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1

Graduate Difficulty with the pullback bundle

  • xaos
  • · Replies 5 ·
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5