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Cycle-parallel real hypersurfaces of quaternionic projective space [PDF]

open access: yesTsukuba Journal of Mathematics, 1993
A hypersurface \(M\) of a Riemannian manifold \(A\) is said to be cyclic- parallel, if its shape operator \(A\) satisfies \({\mathfrak S} \langle (\nabla_ X A)Y, Z\rangle = 0\) for all \(X\), \(Y\), \(Z\) tangent to \(M\) where \(\mathfrak S\) denotes the cyclic sum with respect to \(X\), \(Y\), \(Z\). In the paper the following is proved: Let \(N\) be
openaire   +3 more sources

A characterization of Einstein real hypersurfaces in quaternionic projective space

open access: yesTsukuba Journal of Mathematics, 1998
In this paper, the authors generalize a result proven previously by the second author. They prove that a real hypersurface \(M\) of the quaternionic projective space is an Einstein manifold if and only if it satisfies a certain cyclic sum which involves the curvature and the Ricci tensors of \(M\) and two orthogonal distributions defined by the ...
Lee, Soo Hyo   +2 more
openaire   +4 more sources

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