| Autor: |
Gilkey, P., Nikcevic, S., Westerman, D. |
| Rok vydání: |
2008 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic (resp. C-k for finite k at least 2) pseudo-Riemannian metric on M defined near P. We construct a torsion free real analytic (resp. C-k) connection D which is defined near P on the tangent bundle of M whose curvature operator is the given operator R at P and so that D has constant scalar curvature. We show that if R is Ricci symmetric, then D can be chosen to be Ricci symmetric; if R has trace free Ricci tensor, then D can be chosen to have trace free Ricci tensor; if R is Ricci alternating, then D can be chosen to be Ricci alternating. |
| Databáze: |
arXiv |
| Externí odkaz: |
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