Recent content by zhangzujin

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    Incompressiblitiy and unit length implies constants

    Year, the question is originated from vector analysis, then all functions are smooth, i.e. infinitely differentiable.Thank you.
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    Incompressiblitiy and unit length implies constants

    I mean if X=(u,v) =(u(x,y),v(x,y)) satisifies 1. |X|=1; 2. div X=0; then X is a constant, i.e. idependent of x,y.
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    Incompressiblitiy and unit length implies constants

    Thank HallsofIvy for reminding...And (u)^2 is just the square of u, same as the meaning of (v)^2...
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    Incompressiblitiy and unit length implies constants

    Any guys here knows? Thank you...
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    Do Products of L^2 Functions Converge in the Integral?

    g,h \in L^2, then gh\in L^1 by Holder inequality. and so I do not know the integral \int_K fgh is well-defined?
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    Incompressiblitiy and unit length implies constants

    Let u,v\in C^1(R^2), and (u)^1+(v)^2=1,\partial_x u+ \partial_y v=0. Then u,v are constants. Is it right? How to prove?
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    Is There a Unique Torsion-Free Affine Connection on a Lie Group?

    Aha. Of course not. I'm just reading Riemannian Geometry by Petersen, interested in the exercises of that. In fact, my major is PDEs.
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    Is There a Unique Torsion-Free Affine Connection on a Lie Group?

    [SIZE="5"][FONT="Comic Sans MS"][FONT="Courier New"]Let G be a Lie group. Show that there exists a unique affine connection such that \nabla X=0 for all left invariant vector fields. Show that this connection is torsion free iff the Lie algebra is Abelian.
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