- #1
hedipaldi
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Hi,
are there two non isomorphic surfaces with the same gaussian curvature?
thank's
Hedi
are there two non isomorphic surfaces with the same gaussian curvature?
thank's
Hedi
hedipaldi said:Hi,
are there two non isomorphic surfaces with the same gaussian curvature?
thank's
Hedi
hedipaldi said:Hi,
are there two non isomorphic surfaces with the same gaussian curvature?
thank's
Hedi
mathwonk said:I assumed the question meant: is a diffeomorphism that preserves gauss curvature also an isometry?
mathwonk said:I assumed the question meant: is a diffeomorphism that preserves gauss curvature also an isometry?
Surfaces with same Gaussian curvature are surfaces that have the same curvature at all points on their surface. This means that if a circle is drawn on these surfaces, the curvature at every point on the circle will be the same.
Surfaces with same Gaussian curvature are important because they have the same intrinsic geometry, which allows for certain properties and calculations to be easily determined. They also have applications in fields such as differential geometry and physics.
Hedi's question asks if there exists a surface with constant Gaussian curvature that is not a plane, sphere, or pseudosphere. Surfaces with same Gaussian curvature are related to this question because they all have a constant Gaussian curvature.
Yes, surfaces with same Gaussian curvature can have different shapes. This is because the Gaussian curvature only describes the curvature at each point on the surface, not the overall shape of the surface.
Yes, there are many real-life examples of surfaces with same Gaussian curvature. Some examples include the surface of a sphere, the surface of a cylinder, and the surface of a cone. These surfaces all have a constant Gaussian curvature, making them examples of surfaces with same Gaussian curvature.