User Vladimir S Matveev

5 votes

Reference for when a metric on a four-manifold is Kahler?

answered Oct 11, 2014 at 12:39

5 votes

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Vector fields $X$ and $Y$ commute on a closed set $K$. Do there exist commuting $\tilde X,\tilde Y$ with $\tilde X=X$ and $\tilde Y=Y$ on $K$?

answered Dec 4, 2022 at 16:25

4 votes

If there exists a function on a Riemannian manifold such that its Hessian matrix is the identity matrix?

answered Feb 10, 2023 at 9:48

4 votes

On a parallelizable manifold, is there always a frame satisfying $[X_i,X_j]=0$?

answered May 17, 2016 at 18:36

4 votes

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Applications of Hessian operator in the Riemann manifold. Simple samples $S_{2}(f)$

answered May 17, 2016 at 19:57

4 votes

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Geodesic flows and Killing fields

answered Nov 29 at 11:35

4 votes

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Generic absence of non-trivial first integrals of geodesic flows

answered Aug 19, 2014 at 6:31

4 votes

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Hamiltonian flow local diffeomorphism?

answered Jul 22, 2015 at 18:03

4 votes

Are compact, complex, affinely flat manifolds geodesically complete?

answered Sep 16, 2015 at 7:11

4 votes

Volume-preserving projective transformations are isometries

answered Mar 21, 2014 at 11:17

4 votes

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Transitive geodesics on closed surfaces of genus greater than one

answered Aug 7, 2013 at 16:33

3 votes

Does identical scalar curvature imply isometric?

answered Oct 1, 2013 at 19:50

3 votes

Intuition for Levi-Civita connection via Hamiltonian flows

answered Apr 12, 2013 at 6:35

3 votes

Holonomy of compact manifolds

answered Apr 11, 2012 at 7:49

3 votes

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Are there hermitian metrics with the volume form of a Kahler metric?

answered Apr 16, 2012 at 10:51

3 votes

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Large and Small Conformal Groups

answered Sep 11, 2014 at 7:54

3 votes

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Normalized packing number

answered Dec 13, 2013 at 11:42

3 votes

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Global conformal equivalence of two regions of Minkowski spacetime

answered Nov 26, 2013 at 19:22

3 votes

Diameter of a convex body relative to its Legendre ellipsoid

answered Oct 11, 2015 at 16:51

3 votes

List of generic properties of Riemannian metrics

answered Nov 3, 2015 at 14:37

3 votes

Connections having the same holonomy along loops at a point

answered Mar 23, 2015 at 18:20

3 votes

Curvature of singular Riemannian metric

answered Dec 14, 2022 at 11:43

2 votes

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Obstructions to maximal number of independent constants of motion in a given symplectic manifold

answered Apr 21, 2023 at 6:22

2 votes

Comparing diffusion processes in different metrics

answered Nov 18, 2022 at 14:11

2 votes

Smoothness of the fourth power of the geodesic distance in a Finsler geometry

answered Oct 17, 2015 at 20:42

2 votes

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Cusps as warped products

answered Nov 18, 2013 at 15:48

2 votes

vector field on a curve as projection of a constant vector field on an embedding space

answered Apr 26, 2014 at 10:23

2 votes

Ellipse naturally associated with a polygon

answered May 6, 2012 at 17:25

2 votes

For what metrics are circles solutions of the isoperimetric problem?

answered Jun 28, 2012 at 16:22

2 votes

Every real-holomorphic Hamiltonian vector field on a Kähler manifold is Killing (and preserves curvature), yes?

answered Aug 16, 2013 at 10:37

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66 Answers

Reference for when a metric on a four-manifold is Kahler?

Vector fields $X$ and $Y$ commute on a closed set $K$. Do there exist commuting $\tilde X,\tilde Y$ with $\tilde X=X$ and $\tilde Y=Y$ on $K$?

If there exists a function on a Riemannian manifold such that its Hessian matrix is the identity matrix?

On a parallelizable manifold, is there always a frame satisfying $[X_i,X_j]=0$?

Applications of Hessian operator in the Riemann manifold. Simple samples $S_{2}(f)$

Geodesic flows and Killing fields

Generic absence of non-trivial first integrals of geodesic flows

Hamiltonian flow local diffeomorphism?

Are compact, complex, affinely flat manifolds geodesically complete?

Volume-preserving projective transformations are isometries

Transitive geodesics on closed surfaces of genus greater than one

Does identical scalar curvature imply isometric?

Intuition for Levi-Civita connection via Hamiltonian flows

Holonomy of compact manifolds

Are there hermitian metrics with the volume form of a Kahler metric?

Large and Small Conformal Groups

Normalized packing number

Global conformal equivalence of two regions of Minkowski spacetime

Diameter of a convex body relative to its Legendre ellipsoid

List of generic properties of Riemannian metrics

Connections having the same holonomy along loops at a point

Curvature of singular Riemannian metric

Obstructions to maximal number of independent constants of motion in a given symplectic manifold

Comparing diffusion processes in different metrics

Smoothness of the fourth power of the geodesic distance in a Finsler geometry

Cusps as warped products

vector field on a curve as projection of a constant vector field on an embedding space

Ellipse naturally associated with a polygon

For what metrics are circles solutions of the isoperimetric problem?

Every real-holomorphic Hamiltonian vector field on a Kähler manifold is Killing (and preserves curvature), yes?