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THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
Perez Juan De Dios,Suh Young-Jin Korean Mathematical Society 2007 대한수학회지 Vol.44 No.1
In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.
Killing structure Jacobi operator of a real hypersurface in a complex projective space
Juan de Dios Perez 대한수학회 2021 대한수학회지 Vol.58 No.2
We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the $k$-th generalized Tanaka-Webster connection.
De Dios Perez, Juan,Santos, Florentino Garcia Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.2
We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition.
Recurrent Jacobi operator of real hypersurfaces in complex two-plane Grassmannians
정임순,Juan de Dios Perez,Young Jin Suh 대한수학회 2013 대한수학회보 Vol.50 No.2
In this paper we give a non-existence theorem for Hopf hy- persurfaces in the complex two-plane Grassmannian G2(Cm+2) with re- current normal Jacobi operator ¯RN.
Konstantina Panagiotidou,Juan de Dios Perez 대한수학회 2015 대한수학회보 Vol.52 No.5
In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ξ are studied.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
Jeong, Imsoon,Perez, Juan De Dios,Suh, Young Jin Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this paper we give a non-existence theorem for Hopf hypersurfaces in the complex two-plane Grassmannian $G_2({\mathbb{C}}^{m+2})$ with re-current normal Jacobi operator ${\bar{R}}_N$.
PANAGIOTIDOU, KONSTANTINA,PEREZ, JUAN DE DIOS Korean Mathematical Society 2015 대한수학회보 Vol.52 No.5
In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.
ON A CHARACTERIZATION OF REAL HYPERSURFACES OF TYPE A IN A QUATERNIONIC PROJECTIVE SPACE
KI, U-HANG,PEREZ, Juan De Dios,SUH, Young Jin 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.5 No.-
In this paper, under certain conditions on the orthogonal distribution D, we give a characterization of real hypersurfaces of type A in a quaternionic projective space QP^(m).
REAL HYPERSURFACES IN COMPLEX SPACE FORMS WITH ε-PARALLEL RICCI TENSOR AND STRUCTURE JACOBI OPERATOR
Ki, U-Hang,Perez Juan De Dios,Santos Florentino G.,Suh Young-Jin Korean Mathematical Society 2007 대한수학회지 Vol.44 No.2
We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.