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Keywords = Lorentzian submanifold

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14 pages, 302 KiB  
Article
On Surfaces of Exceptional Lorentzian Lie Groups with a Four-Dimensional Isometry Group
by Giovanni Calvaruso and Lorenzo Pellegrino
Mathematics 2025, 13(15), 2529; https://doi.org/10.3390/math13152529 - 6 Aug 2025
Abstract
In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian. In this paper, we prove the non-existence of parallel and totally [...] Read more.
In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian. In this paper, we prove the non-existence of parallel and totally umbilical (in particular, totally geodesic) surfaces for three-dimensional Lorentzian Lie groups, which admit a four-dimensional isometry group, but are neither of Bianchi–Cartan–Vranceanu-type nor homogeneous plane waves. Consequently, the results of the present paper complete the investigation of these fundamental types of surfaces in all homogeneous Lorentzian manifolds, whose isometry group is four-dimensional. As a byproduct, we describe a large class of flat surfaces of constant mean curvature in these ambient spaces and exhibit a family of examples. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
18 pages, 346 KiB  
Article
Pinching Results for Submanifolds in Lorentzian–Sasakian Manifolds Endowed with a Semi-Symmetric Non-Metric Connection
by Mohammed Mohammed, Ion Mihai and Andreea Olteanu
Mathematics 2024, 12(23), 3651; https://doi.org/10.3390/math12233651 - 21 Nov 2024
Viewed by 844
Abstract
We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space [...] Read more.
We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space form. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
18 pages, 303 KiB  
Article
On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection
by Majid Ali Choudhary, Khaled Mohamed Khedher, Oğuzhan Bahadır and Mohd Danish Siddiqi
Mathematics 2021, 9(19), 2430; https://doi.org/10.3390/math9192430 - 30 Sep 2021
Cited by 9 | Viewed by 1973
Abstract
This research deals with the generalized symmetric metric U-connection defined on golden Lorentzian manifolds. We also derive sharp geometric inequalities that involve generalized normalized δ-Casorati curvatures for submanifolds of golden Lorentzian manifolds equipped with generalized symmetric metric U-connection. Full article
(This article belongs to the Special Issue Analytic and Geometric Inequalities: Theory and Applications)
12 pages, 235 KiB  
Article
Pseudo-Isotropic Centro-Affine Lorentzian Surfaces
by Olivier Birembaux
Mathematics 2020, 8(8), 1284; https://doi.org/10.3390/math8081284 - 4 Aug 2020
Cited by 5 | Viewed by 1715
Abstract
In this paper, we study centro-affine Lorentzian surfaces M2 in 3 which have pseudo-isotropic or lightlike pseudo-isotropic difference tensor. We first show that M2 is pseudo-isotropic if and only if the Tchebychev form T=0. In that case, [...] Read more.
In this paper, we study centro-affine Lorentzian surfaces M2 in 3 which have pseudo-isotropic or lightlike pseudo-isotropic difference tensor. We first show that M2 is pseudo-isotropic if and only if the Tchebychev form T=0. In that case, M2 is a an equi-affine sphere. Next, we will get a complete classification of centro-affine Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isotropic. Full article
(This article belongs to the Special Issue Riemannian Geometry of Submanifolds)
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