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Title of Journal: J Geom

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Abbravation: Journal of Geometry

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Springer Basel

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DOI

10.1016/0002-9394(65)92007-6

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1420-8997

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Rakić duality principle in the almost Hermitian ge

Authors: Maria Ivanova Vesselin Videv Zhivko Zhelev
Publish Date: 2013/07/12
Volume: 104, Issue: 3, Pages: 495-504
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Abstract

Rakić duality principle turns out to be one of the crucial steps in proving Osserman conjecture Basically it claims that if mathcalR is an Osserman algebraic curvature tensor and X and Y are unit vectors then Y is an eigenvector of the Jacobi operator mathcalRcdot XX if and only if X is an unit eigenvector of mathcalRcdot YY with the same eigenvalue We prove necessary and sufficient conditions for certain almost Hermitian manifolds the so called AH 3manifolds to have pointwise constant holomorphic curvature and pointwise constant antiholomorphic sectional curvature It turns out that for this class of almost Hermitian manifolds these conditions are directly connected to the duality principle

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Other Papers In This Journal:
  1. A New Class of Translation Planes Constructed by Hyper-regulus Replacement
  2. Propellers in Affine Cayley–Klein Planes
  3. On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds
  4. Deformation of minimal surfaces with planar curvature lines
  5. On compact semisimple Lie groups as 2-plectic manifolds
  6. An axiomatic look at the Erdős-Trost problem
  7. An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
  8. Linearly small elation quadrangles
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