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Anthony Carapetis
  • Member for 10 years, 2 months
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68 votes
Accepted

Understanding the Laplace operator conceptually

52 votes
Accepted

What is the flaw in my thinking for the graph of this function?

25 votes
Accepted

Why do we think of a vector as being the same as a differential operator?

17 votes
Accepted

Intuition on Kulkarni-Nomizu product

16 votes

Prove that if a linear operator is continuous, then it is bounded.

16 votes
Accepted

Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?

15 votes
Accepted

mean curvature is trace of second fundamental form?

15 votes

If a plane curve has curvature bounded from below, is it contained in a disk?

14 votes

Adjoint of the covariant derivative on a Riemannian manifold

14 votes

Kato's inequality

13 votes

Notation: What does this summation mean?

13 votes

Geometrical interpretation of Ricci curvature

13 votes

divergence of a vector field on a manifold

13 votes

Shortest path between two points on a surface

13 votes
Accepted

Is this contraction of metric tensor derivatives symmetric?

13 votes
Accepted

Why is the Sasaki metric natural?

13 votes

Since the Curvature tensor depends on a connection (not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?

12 votes
Accepted

Coordinate independence of geometrical objects.

12 votes

Differentiability of the distance function

12 votes
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Lie vs. covariant derivative: Visual motivation

12 votes

Isometry of Torus

11 votes
Accepted

Second (and higher) derivatives of maps between manifolds

11 votes
Accepted

why not the Ricci tensor is the contraction of first and second indices of Riemann tensor

11 votes
Accepted

$f:\bf S^1 \to \bf R$, there exist uncountably many pairs of distinct points $x$ and $y$ in $\bf S^1$ such that $f(x)=f(y)$? (NBHM-2010)

11 votes

Is the tangent bundle still a manifold if we equip it with the disjoint union topology?

11 votes
Accepted

Commutator of laplacian and covariant derivative of a tensor

10 votes

Commutation of covariant derivative of functions

10 votes

What is the motivation of Measure Theory when there is probability theory?

10 votes

When does gradient flow not converge?

10 votes
Accepted

Are all metric tensors diagonal?

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