Vladimir S Matveev
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Registered User
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Jun 3 |
awarded | ● Critic |
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May 19 |
comment |
Surface locally isometric to a sphere. The "Riemmanian" version of the question is not that trivial IMHO. A possible proof: the gauss curvature of the surface is constant because it is preserved by the isometries. It is positive since every compact surface must have a point where the curvature is positive. Then, the surface is diffeomorph to the sphere or to the projective plane. The latter can not be imbedded in $R^3$ (and the proof of this fact is much easier under the assumption that the curvature is positive) so the surface is the sphere. Now, by the Alexandrov theorem the sphere is standartly imbedded. |
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Apr 25 |
awarded | ● Necromancer |
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Apr 19 |
awarded | ● Yearling |
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Apr 12 |
revised |
Intuition for Levi-Civita connection via Hamiltonian flows edited body |
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Apr 12 |
answered | Intuition for Levi-Civita connection via Hamiltonian flows |
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Mar 29 |
accepted | Alternative Almost Complex Structures |
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Mar 26 |
answered | Alternative Almost Complex Structures |
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Feb 21 |
comment |
Projectively equivalent connections The classical sources on projectively equivalent connections are Levi-Civita: Sulle trasformazioni delle equazioni dinamiche. Ann. di Mat., serie 2a. 24, 55–300 (1896). English transl. in Regular and Chaotic Dynamics 14, 580–614 (2009) and Thomas, T. Y.: On the projective and equi-projective geo metries of paths. Proc. Natl. Acad. Sci. USA 11, 199–203 (1925) In recent time projectively equivalent connections were actively studied in the framework of parabolic geometries; see the survey M. Eastwood, Notes on projective differential geometry, arXiv:0806.3998 Everything IMHO |
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Feb 20 |
accepted | Projectively equivalent connections |
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Feb 19 |
answered | Projectively equivalent connections |
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Jan 26 |
answered | Tensor contraction and Covariant Derivative |
