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