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# Real Hypersurfaces in Complex Two-plane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection

Published:2016-06-24
Printed: Dec 2016
• Juan de Dios Pérez,
• Hyunjin Lee,
Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 702-701, Republic of Korea
• Young Jin Suh,
Department of Mathematics and Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 702-701, Republic of Korea
• Changhwa Woo,
Department of Mathematics, Kyungpook National University , Daegu 702-701, Republic of Korea
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## Abstract

There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce the notion of generalized Tanaka-Webster (in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface $M$ in $G_2({\mathbb C}^{m+2})$. Next, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with GTW Reeb parallel Ricci tensor.
 Keywords: Complex two-plane Grassmannian, real hypersurface, Hopf hypersurface, generalized Tanaka-Webster connection, parallelism, Reeb parallelism, Ricci tensor
 MSC Classifications: 53C40 - Global submanifolds [See also 53B25] 53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)

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