Isometric immersions of space forms into Sp×R
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DOI: 10.1002/mana.201800571
Abstract: In this article we classify isometric immersions f:Mn(c)→Sn+p×R of Riemannian manifolds of dimension n and constant sectional curvature c≤1 into the product space Sn+p×R, p≤n−3, where Sm denotes the m‐dimensional unit sphere. read more here.
Keywords: isometric immersions; immersions space; space; space forms ... See more keywords
Classification of $$\eta $$η-Biharmonic Surfaces in Non-flat Lorentz Space Forms
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DOI: 10.1007/s00009-018-1250-5
Abstract: In this paper, we prove that $$\eta $$η-biharmonic surfaces in non-flat three-dimensional Lorentz space forms are isoparametric and give full classification results. read more here.
Keywords: non flat; eta biharmonic; lorentz space; biharmonic surfaces ... See more keywords
An improved first Chen inequality for Legendrian submanifolds in Sasakian space forms
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DOI: 10.1007/s10998-016-0161-0
Abstract: Legendrian submanifolds in Sasakian space forms play an important role in contact geometry. Defever et al. (Boll Unione Mat Ital B 7(11):365–374, 1997) established the first Chen inequality for C-totally real submanifolds in Sasakian space… read more here.
Keywords: submanifolds sasakian; legendrian submanifolds; sasakian space; first chen ... See more keywords
r-Almost Newton–Ricci solitons on Legendrian submanifolds of Sasakian space forms
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DOI: 10.1007/s10998-021-00394-x
Abstract: We establish the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton–Ricci solitons (r-anrs) with the potential function $$\psi : M^{n} \rightarrow \mathcal {R}$$ . Also, we discuss the Legendrian… read more here.
Keywords: submanifolds sasakian; legendrian submanifolds; ricci solitons; sasakian space ... See more keywords
Second-Order Parallel Tensors on ????-Manifolds and Semiparallel Hypersurfaces of ????-Space Forms
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DOI: 10.1007/s11253-020-01735-8
Abstract: We study a second-order parallel symmetric tensor in an ????-manifold and show that there is no semiparallel hypersurface in the ????-space forms M ˜ 2 n + s c $$ {\tilde{M}}^{2n+s}(c) $$ with c ≠… read more here.
Keywords: second order; order parallel; parallel tensors; space forms ... See more keywords
Curvature estimate of steepest descents of 2-dimensional maximal space-like hypersurfaces on space forms
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DOI: 10.1007/s11464-020-0826-0
Abstract: For the maximal space-like hypersurface defined on 2-dimensional space forms, based on the regularity and the strict convexity of the level sets, the steepest descents are well defined. In this paper, we come to estimate… read more here.
Keywords: space; steepest descents; maximal space; curvature estimate ... See more keywords
On biharmonic hypersurfaces in 6-dimensional space forms
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DOI: 10.1007/s13370-019-00714-y
Abstract: We study biharmonic hypersurfaces in the space forms $$\overline{M}^{6}(c)$$ with at most four distinct principal curvatures and whose second fundamental form is of constant norm. We prove that every such biharmonic hypersurface in $$\overline{M}^{6}(c)$$ has… read more here.
Keywords: space; biharmonic hypersurface; every biharmonic; biharmonic hypersurfaces ... See more keywords
Hypersurfaces with constant scalar curvature in space forms
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DOI: 10.1016/j.difgeo.2018.01.001
Abstract: Abstract In this paper we study the rigidity of complete hypersurfaces with constant scalar curvature in Riemannian space forms. Under an appropriate constraint on Φ, the traceless part of its second fundamental form, we prove… read more here.
Keywords: scalar curvature; hypersurfaces constant; constant scalar; space forms ... See more keywords
Totally biharmonic hypersurfaces in space forms and 3-dimensional BCV spaces
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DOI: 10.1142/s0129167x21500257
Abstract: A hypersurface is said to be totally biharmonic if all its geodesics are biharmonic curves in the ambient space. We prove that a totally biharmonic hypersurface into a space form is an isoparametric biharmonic hypersurface,… read more here.
Keywords: hypersurfaces space; space forms; totally biharmonic; biharmonic hypersurfaces ... See more keywords
Biwarped product submanifolds of complex space forms
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DOI: 10.1142/s0219887819500725
Abstract: The class of biwarped product manifolds is a generalized class of product manifolds and a special case of multiply warped product manifolds. In this paper, biwarped product submanifolds of the type [Formula: see text] embedded… read more here.
Keywords: complex space; biwarped product; product submanifolds; space forms ... See more keywords
Chen inequalities for submanifolds of complex space forms and Sasakian space forms with quarter-symmetric connections
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DOI: 10.1142/s0219887819501184
Abstract: In this paper, we obtain Chen’s inequalities for submanifolds of complex space forms and Sasakian space forms with quarter-symmetric connections. read more here.
Keywords: complex space; space forms; inequalities submanifolds; submanifolds complex ... See more keywords