Pseudo Riemannian manifolds whose generalized Jacobi operator has constant characteristic polynomial |
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| Authors: | P Gilkey G Stanilov V Videv |
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| Institution: | (1) Mathematics Department, University of Oregon, 97403 Eugene, Or, USA;(2) Mathematics Department, Thracian University, University Campus, 6000 Stara, Zagora, Bulgaria;(3) Faculty of Mathematics and Informatics, University of Sofia, 5 James Bourchier Blvd, 1164 Sofia, Bulgaria |
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| Abstract: | Letg be a non-degenerate innerproduct of signature (p,q) onR
m
. LetGr
r,s
(g) be the Grassmanian of planes  so the restriction of g to is non-degenerate and has signature (r, s). IfR is an algebraic curvature tensor onR
m
, we define a generalized Jacobi operator onGr
r,s
(g) and study when the characteristic polynomial of this operator is constant.Dedicated to Professor Helmut Karzel on his 70th birthdayResearch partially supported by the NSF (USA).Research partially supported by the NFSI (Bulgaria). |
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| Keywords: | Primary 53A15 53C05 |
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