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
Myers’ type theorem with the Bakry–Émery Ricci tensor
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DOI: 10.1007/s10455-018-9613-5
Abstract: In this paper, we prove a new Myers’ type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry–Émery Ricci tensor has a positive lower bound. The… read more here.
Keywords: bakry mery; mery ricci; myers type; ricci tensor ... See more keywords
Labeling spherically symmetric spacetimes with the Ricci tensor
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DOI: 10.1088/1361-6382/aa525d
Abstract: We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27 205024]. In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze… read more here.
Keywords: spherically symmetric; labeling spherically; symmetric spacetimes; tensor ... See more keywords
Stability of non-degenerate Ricci-type Palatini theories
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DOI: 10.1088/1475-7516/2023/04/014
Abstract: We study the stability of theories where the gravitational action has arbitrary algebraic dependence on the three first traces of the Riemann tensor: the Ricci tensor, the co-Ricci tensor, and the homothetic curvature tensor. We… read more here.
Keywords: stability; ricci tensor; ricci; ricci type ... See more keywords
The Bakry-Émery Ricci Tensor: Application to Mass Distribution in Space-time
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DOI: 10.1134/s0202289321010096
Abstract: Abstract The Bakry-Émery Ricci tensor gives an analogue of the Ricci tensor for a Riemannian manifold with a smooth function. This notion motivates a new version of Einstein’s field equation in which the mass becomes… read more here.
Keywords: ricci; bakry mery; mery ricci; ricci tensor ... 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