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Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor

Published online by Cambridge University Press:  27 November 2012

Young Jin Suh
Young Jin Suh*
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702 701, Republic of Koreayjsuh@knu.ac.kr)
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Abstract

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We introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grassmannians G2(ℂm+2) from the Gauss equation. We then derive a new formula for the Ricci tensor of M in G2(ℂm+2). Finally, we prove that there does not exist any Hopf real hypersurface in complex two-plane Grassmannians G2(ℂm+2) with parallel Ricci tensor.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 6 , December 2012 , pp. 1309 - 1324
Copyright
Copyright © Royal Society of Edinburgh 2012