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346699
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10 votes
2 answers
1k views

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated?

8 votes
2 answers
702 views

Is there some Riemannian manifold's version of Whitney theorem?

7 votes
5 answers
4k views

Can anyone give an example of Ricci flat Riemannian or Lorentzian Manifold that is not flat?

6 votes
1 answer
220 views

Question about conjugate points

6 votes
2 answers
587 views

The necessary and sufficient condition for $\textbf{global}$ conformal flatness of a n-dim (pseudo-)Riemannian manifold

6 votes
1 answer
713 views

Tangent space describes the manifold's first order characteristic. Is there something like tangent space describes higher order characteristic?

6 votes
1 answer
746 views

Does there exist finite dimensional irreducible representation of Euclidean or Poincare group in which translation and rotation both act nontrivially?

5 votes
2 answers
2k views

How to calculate the square root of matrix $A+B$ perturbatively?

4 votes
1 answer
1k views

How to calculate the fundamental group of general configuration space

4 votes
2 answers
1k views

Lie group about the quantum harmonic oscillator [closed]

3 votes
1 answer
834 views

If there exists a nontrivial vector field $V$ such that $\nabla_{X}V=0$ for any vector field $X$, the manifold must be flat?

3 votes
2 answers
404 views

In what condition is a conformal flat manifold flat?

3 votes
1 answer
291 views

Reference for real and complex projective representation of finite group

2 votes
0 answers
181 views

How many linear independent vector fields can be constructed on a general manifold with $\chi(M)=0$?

1 vote
2 answers
508 views

Are there some websites for self learining of advanced mathematics? [closed]

1 vote
1 answer
409 views

Which book will discuss torsion tensor and affine connection in detail? [closed]

0 votes
2 answers
422 views

Can simply or not simply connected maximally symmetric (Semi-)Riemannian manifold be completely classified?