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Deane
  • Member for 11 years, 1 month
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12 votes
Accepted

Why must differential forms be antisymmetric?

9 votes
Accepted

On the definition of a tensor in the study of manifolds

9 votes
Accepted

What's the intuition behind the Co-Area formula?

8 votes
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Deduce the shape of a manifold from the Riemannian metric

5 votes
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Is the differential $\mathrm{d}\vec{r}$ a sensible mathematical object?

4 votes
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Regular value of the determinant map

4 votes

Explanation about frames as distinct from a co-ordinate system

4 votes
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Neighbourhood of Linearly Independent Vector Fields $(X_1,\dots,X_n)$

4 votes
Accepted

Can we define a specific metric tensor to all manifolds?

4 votes

How to understand $R^{\rho}_{\sigma\mu\nu}$ for constructing geometries?

4 votes

Exterior Derivative of One-Form vs Torsion of Connection

4 votes
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Local isometric immersion from $\mathbb H^{n}$ into $\mathbb R^{2n-1}$

4 votes
Accepted

How to understand the explanation of conjugate point in Petersen's Riemannian geometry

4 votes
Accepted

Warped Product Metric: assumption on the metric

4 votes

Trace and Lie derivative of a $(1,1)$-tensor commute (Direct proof)

4 votes

Analytic definition implies geometric definition of trigonometric functions

3 votes

Conceptual understanding of Christoffel symbols

3 votes

Different approaches to $g\left(\nabla_{\nabla_{e_j}e_i}X,e_i\right)+g\left(\nabla_{e_i}X,\nabla_{e_j}e_i\right)=0$.

3 votes
Accepted

Busemann function and its relation to horocycle

3 votes
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Why we define connection on a vector bundle in such an unnatural way?

3 votes

Definitions of Hessian in Riemannian Geometry

3 votes
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Second order derivatives: Exterior and Lie

3 votes
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Einstein 3-manifold has constant sectional curvature

3 votes

Limit definition of the exterior derivative

3 votes
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On $C^1$ convex domain

3 votes
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Meaning of degenerate PDE

3 votes

An 'obvious' inequality in Mean curvature flow

2 votes
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Ricci flow as heat flow on Riemannian manifold

2 votes

Lie algebra of $\mathrm{SL}(2, \mathbb{C})$ using method of differential geometry

2 votes
Accepted

Practical Uses for the Tensor Product