Published in Open Mathematics
In this paper, we introduce and study Golden-like statistical manifolds. We obtain some basic inequalities for curvature invariants of statistical submanifolds in Golden-like statistical manifolds. Also, in support of our definition, we provide a couple of examples.
Published in Afrika Matematika
The purpose of this paper is to study properties of hypersurfaces of a Riemannian manifold equipped with a golden structure. We discuss the necessary and sufficient conditions for a hypersurface to be a golden Riemannian manifold in terms of invariance. The totally geodesics and totally umbilical hypersurfaces in golden Riemannian manifolds are ana...
Published in General Relativity and Gravitation
This article deals with the investigation of geometric properties in terms of curvatures of Lemaître–Tolman–Bondi (briefly, LTB) spacetime (Lemaître 1933; Tolman 1934; Bondi 1947), an inhomogeneous cosmological model of the universe. It is shown that LTB spacetime is an Einstein manifold of level 3, 2-quasi Einstein and generalized Roter type manif...
Published in Partial Differential Equations and Applications
Let K=R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {K}}= {\mathbb {R}}$$\end{document} or C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
Published in Results in Mathematics
In this paper, we classify pseudo-isotropic Lorentzian centroaffine hypersurfaces whose difference tensor satisfies the condition K2≠0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \beg...
Published in Journal of Geometry
Lee and Suh (Proc R Soc Edinb Sect A, 2021, https://doi.org/10.1017/prm.2020.83) proved that there do not exist Hopf hypersurfaces with parallel Ricci tensor in the complex quadric Qm=SOm+2/SOmSO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsf...
Published in Mediterranean Journal of Mathematics
We study the hypersurfaces of S3×S3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {S}}^3 \times {\mathbb {S}}^3$$\end{document} with a specially chosen P\docu...
Published in Results in Mathematics
In this paper, we study the geometry of pointwise semi-slant warped products in a locally conformal Kaehler manifold. In particular, we obtain several results which extend Chen’s inequality for CR-warped product submanifolds in Kaehler manifolds. Also, we study the corresponding equality cases. Several related results on pointwise semi-slant warped...
Published in Mediterranean Journal of Mathematics
We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a...
We investigate curved flats in Lie sphere geometry. We show that in this setting curved flats are in one-to-one correspondence with pairs of Demoulin families of Lie applicable surfaces related by Darboux transformation.
