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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 PĂ©rez,
    Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain
  • 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 Complex two-plane Grassmannian, real hypersurface, Hopf hypersurface, generalized Tanaka-Webster connection, parallelism, Reeb parallelism, Ricci tensor
MSC Classifications: 53C40, 53C15 show english descriptions Global submanifolds [See also 53B25]
General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C40 - Global submanifolds [See also 53B25]
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
 

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