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On the Geometry of the Null Tangent Bundle of a Pseudo-Riemannian Manifold

Axioms, 2023
When we consider a non-definite pseudo-Riemannian manifold, we obtain lightlike tangent vectors that constitute the null tangent bundle, whose fibers are lightlike cones in the corresponding tangent spaces.
Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz, Giovanni Calvaruso   +2 more
doaj   +1 more source

Affine transformations of the tangent bundle of a common path space

Дифференциальная геометрия многообразий фигур, 2023
In this paper, we study infinitesimal transformations of the tangent bundle of a common path space. The general path space is a genera­liza­tion space of the affine connectivity.
N. D. Nikitin, O. G. Nikitina
doaj   +1 more source

Natural Ricci Solitons on Tangent and Unit Tangent Bundles [PDF]

Zurnal matematiceskoj fiziki, analiza, geometrii, 2021
Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure on the base manifold.
Abbassi, Mohamed Tahar Kadaoui, Amri, Noura   +1 more
openaire   +3 more sources

Lifts of Hypersurfaces on a Sasakian Manifold with a Quartersymmetric Semimetric Connection (QSSC) to Its Tangent Bundle

Universal Journal of Mathematics and Applications, 2023
The aim of the present paper is to introduce a Sasakian manifold immersed with a quartersymmetric semimetric connection to a tangent bundle. Some basic results are given on a Riemannian connection and a QSSC to the tangent bundle on a Sasakian manifold ...
Lovejoy Swapan Kumar Das, Mohammad Nazrul Islam Khan   +1 more
doaj   +1 more source

Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold

Mathematics, 2023
The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in ...
Rajesh Kumar, Lalnunenga Colney, Samesh Shenawy, Nasser Bin Turki   +3 more
doaj   +1 more source

Lifts of a Quarter-Symmetric Metric Connection from a Sasakian Manifold to Its Tangent Bundle

Mathematics, 2022
The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle.
Mohammad Nazrul Islam Khan, Uday Chand De, Ljubica S. Velimirović   +2 more
doaj   +1 more source

Simplicity of tangent bundles of smooth horospherical varieties of Picard number one

Comptes Rendus. Mathématique, 2022
Recently, Kanemitsu has discovered a counterexample to the long-standing conjecture that the tangent bundle of a Fano manifold of Picard number one is (semi)stable. His counterexample is a smooth horospherical variety.
Hong, Jaehyun
doaj   +1 more source

Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles

Axioms, 2023
The purpose of this paper is to find some conditions under which the tangent bundle TM has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical ...
Esmaeil Peyghan, Davood Seifipour, Ion Mihai   +2 more
doaj   +1 more source

Affine Subspace Concentration Conditions [PDF]

Épijournal de Géométrie Algébrique, 2023
We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold for smooth and reflexive polytopes with barycenter at the origin.
Kuang-Yu Wu
doaj   +1 more source

Prolongations of affine connection and horizontal vectors

Дифференциальная геометрия многообразий фигур, 2020
The linear frame bundle over a smooth manifold is considered. The mapping dе defined by the differentials of the first-order frame e is a lift to the normal N, i.
K.V. Polyakova
doaj   +1 more source