Real hypersurfaces in the complex quadric whose structure Jacobi operator is of Codazzi type
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201800184
Abstract: First we introduce the notion of structure Jacobi operator of Codazzi type for real hypersurfaces in the complex quadric Qm=SOm+2/SOmSO2 . Next we give a complete classification of real hypersurfaces in Qm=SOm+2/SOmSO2 with structure Jacobi… read more here.
Keywords: codazzi type; structure jacobi; real hypersurfaces; operator codazzi ... See more keywords
Real Hypersurfaces in the Complex Hyperbolic Quadric with Parallel Ricci Tensor
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DOI: 10.1007/s00025-019-0961-7
Abstract: We introduce the notion of parallel Ricci tensor for real hypersurfaces in the complex hyperbolic quadric $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$Qm∗=SOm,2o/SOmSO2. According to the $$\mathfrak {A}$$A-principal or the $$\mathfrak {A}$$A-isotropic unit normal vector field N, we give… read more here.
Keywords: ricci; hypersurfaces complex; real hypersurfaces; complex hyperbolic ... See more keywords
Classification Theorems for Biharmonic Real Hypersurfaces in a Complex Projective Space
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DOI: 10.1007/s00025-019-1062-3
Abstract: First, we classify proper biharmonic Hopf real hypersurfaces in $\mathbb{C}P^2$. Next, we classify proper biharmonic real hypersurfaces with two distinct principal curvatures in $\mathbb{C}P^n$, where $n\geq 2$. Finally, we prove that biharmonic ruled real hypersurfaces… read more here.
Keywords: hypersurfaces complex; theorems biharmonic; real hypersurfaces; complex projective ... See more keywords
Bounds of generalized normalized $$\delta $$δ-Casorati curvatures for real hypersurfaces in the complex quadric
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DOI: 10.1007/s40065-018-0223-7
Abstract: In the present paper, we first characterize real hypersurfaces in the complex quadric $$Q^{m}$$Qm by giving an inequality in terms of the scalar curvature and the Mean curvature vector field. We also obtain the condition… read more here.
Keywords: delta casorati; casorati curvatures; normalized delta; real hypersurfaces ... See more keywords
Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2
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DOI: 10.1142/s0219887820500735
Abstract: Let M be a three-dimensional real hypersurface in a nonflat complex space form of complex dimension two. In this paper, we prove that M is η-parallel with two distinct principal curvatures at each ... read more here.
Keywords: remarks parallel; real hypersurfaces; parallel real;
On pseudo-Einstein real hypersurfaces
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DOI: 10.1515/advgeom-2019-0024
Abstract: Abstract Let M be a real hypersurface of a complex space form Mn(c) with c ≠ 0 and n ≥ 3. We show that the Ricci tensor S of M satisfies S(X, Y) = ag(X,… read more here.
Keywords: einstein real; pseudo einstein; real hypersurface; real hypersurfaces ... See more keywords
Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians
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DOI: 10.4153/cmb-2017-049-5
Abstract: Abstract On a real hypersurface $M$ in a complex two-plane Grassmannian ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ we have the Lie derivation $\mathcal{L}$ and a differential operator of order one associated with the generalized Tanaka–Webster connection ${{\widehat{\mathcal{L}}}^{\left( k… read more here.
Keywords: complex two; ricci tensor; real hypersurfaces; two plane ... See more keywords
Non-existence of conformally flat real hypersurfaces in both the complex quadric and the complex hyperbolic quadric
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DOI: 10.4153/s0008439521000084
Abstract: Abstract In this paper, by applying for a new approach of the so-called Tsinghua principle, we prove the nonexistence of locally conformally flat real hypersurfaces in both the m-dimensional complex quadric $Q^m$ and the complex… read more here.
Keywords: conformally flat; real hypersurfaces; quadric; complex quadric ... See more keywords