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Search: All articles in the CMB digital archive with keyword structure Jacobi operator

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1. CMB Online first

Kaimakamis, George; Panagiotidou, Konstantina; de Dios Perez, Juan
A classification of three-dimensional real hypersurfaces in non-flat complex space forms in terms of their generalized Tanaka-Webster Lie derivatives
On a real hypersurface $M$ in a non-flat complex space form there exist the Levi-Civita and the k-th generalized Tanaka-Webster connections. The aim of the present paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operator with respect to the Levi-Civita connections coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in directions of any vecro field orthogonal to the structure vector field.

Keywords:$k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator
Categories:53C15, 53B25

2. CMB 2013 (vol 57 pp. 821)

Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin
Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator
In this paper we give a characterization of a real hypersurface of Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb C}^{m+2})} } }$, which means a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in ${G_2({\mathbb C}^{m+2})}$, by the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.

Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator
Categories:53C40, 53C15

3. CMB 2011 (vol 56 pp. 306)

Pérez, Juan de Dios; Suh, Young Jin
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel
We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and satisfies a further condition.

Keywords:complex projective space, real hypersurface, structure Jacobi operator
Categories:53C15, 53C40

4. CMB 2011 (vol 54 pp. 422)

Pérez, Juan de Dios; Suh, Young Jin
Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space
We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time.

Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditions
Categories:53C15, 53B25

5. CMB 2008 (vol 51 pp. 359)

Cho, Jong Taek; Ki, U-Hang
Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator
Real hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type $(A)$ in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator.

Keywords:complex space form, real hypersurface, structure Jacobi operator
Categories:53B20, 53C15, 53C25

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