Kelvin Lois's user avatar
Kelvin Lois's user avatar
Kelvin Lois's user avatar
Kelvin Lois
  • Member for 7 years, 11 months
  • Last seen this week
  • Jakarta, Indonesia
21 votes

Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)

14 votes

Smooth curves on a path connected smooth manifold

14 votes

Prove the Curvature Tensor is a Tensor

14 votes

Extension of Vector field along a curve always exists?

12 votes
Accepted

Completion of local frames for the tangent bundle of a smooth manifold

9 votes
Accepted

Smaller neighborhood around the identity of Lie Group

8 votes

Every path homotopic to a Piecewise linear path (Hatcher 1.1.4)

8 votes
Accepted

Maximal Smooth Atlas For Stereographic Projection

8 votes

Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)

7 votes
Accepted

Lie Derivative of a Metric in Coordinate Expression.

7 votes
Accepted

Dual basis with non-degenerate bilinear form

7 votes

$\operatorname{Lie}(G \times H)\cong \operatorname{Lie}(G)\oplus \operatorname{Lie}(H)$

7 votes
Accepted

Gauss Lemma - Do Carmo's Riemannian geometry, use of parallel transport?

6 votes
Accepted

Corollary 5.39, Lee - Introduction to Smooth Manifolds

6 votes
Accepted

Differential of Multiplication Map of Lie Group

6 votes
Accepted

The dimension of Jacobi field

6 votes

Distance between two points on a surface with metric $g_{mn}$

6 votes
Accepted

How is it that two covariant vectors can be multiplied without one being transposed?

5 votes
Accepted

Is this map $F:V^*\times V\to \mathbb R$ a basis-free definition?

5 votes
Accepted

The union of $x$ and $y$ axis with subspace topology is not locally euclidean

5 votes

Are the spaces $\mathbb{H}^n$ and $\overline{\mathbb{R}}^n_+$ homeomorphic?

5 votes
Accepted

Proving that continuous function $f:[0,2] \to \mathbb{R}$ such as $f(0)=f(2)$, $\exists x \in [0,1]:f(x)=f(x+1)$

5 votes
Accepted

Quotient space of $\mathbb{R}^2$

5 votes
Accepted

Every connected orientable smooth manifold has exactly two orientations, Lee Proposition 15.9

5 votes
Accepted

Continuity of a map to show that differential is full rank in some open set.

4 votes
Accepted

Cartesian product of embeddings is embedding

4 votes
Accepted

Does every smooth local frame of the tangent bundle correspond to a chart?

4 votes
Accepted

Proving John Lee's ISM proposition 5.47. For a smooth real function, each regular sublevel set is a regular domain.

4 votes
Accepted

Gluing vector fields

4 votes
Accepted

Flowout Theorem Part I , John Lee's smooth manifold, page 217.

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