Article
Mathematics, Applied
Oguzhan Bahadir
Summary: In this study, the concept of Sasakian statistical manifold was extended to indefinite Sasakian statistical manifolds. The introduction of lightlike hypersurfaces in indefinite Sasakian statistical manifolds and the establishment of relationships between induced geometrical objects with dual connections were also discussed. Lastly, it was proven that an invariant lightlike submanifold in an indefinite Sasakian statistical manifold is also an indefinite Sasakian statistical manifold.
Article
Mathematics, Applied
Nergiz (Onen) Poyraz
Summary: This study focuses on STCR-lightlike submanifolds of indefinite Sasakian manifolds. Existence and non-existence theorems are proven, and the integrability conditions of various distributions are determined. Characterization theorems for a contact STCR-lightlike submanifold to be a STCR-lightlike product are derived, and some results for minimal contact STCR-lightlike submanifolds of indefinite Sasakian manifolds are found. Examples are also provided.
Article
Physics, Mathematical
S. S. Shukla, Vipul Singh
Summary: In this paper, the concept of radical transversal screen slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds is introduced and studied. The existence theorem, as well as the geometry of the involved distributions, is studied. Additionally, the notion of radical transversal screen semi-slant lightlike submersions is defined, and a characterization theorem is proved. The integrability and totally geodesic foliations of distributions on a fiber of these lightlike submersions are also studied.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Mathematics, Applied
Muqeem Ahmad, Mobin Ahmad, Fatemah Mofarreh
Summary: This paper introduces the concept of a bi-slant lightlike submanifold of a golden semi-Riemannian manifold and provides two examples. It also gives some characterizations about the geometry of such submanifolds.
Article
Mathematics, Applied
Nergiz (Onen) Poyraz
Summary: This article introduces screen generic lightlike submanifolds of indefinite cosymplectic manifolds, investigates the integrability of various distributions, and proves a characterization theorem of such lightlike submanifolds in a cosymplectic space form. We study contact totally umbilical screen generic lightlike submanifolds and minimal screen generic lightlike submanifolds. Examples are also provided.
Article
Mathematics, Applied
Selcen Yuksel Perktas, Adara M. M. Blaga
Summary: In this article, the authors investigate sequential warped product submanifolds of Sasakian manifolds, focusing on the case where the sequential warped product contains one invariant, one pointwise slant, and one anti-invariant submanifold. They provide nonexistence results for this particular scenario and deduce properties and establish Chen's inequality in the two possible cases.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
S. S. Shukla, Akhilesh Yadav
Summary: This paper introduces the notion of radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds and provides a characterization theorem and non-trivial examples. Integrability conditions for distributions on these submanifolds have been obtained, along with necessary and sufficient conditions for foliations to be totally geodesic.
Article
Mathematics
Bang-Yen Chen, Siraj Uddin, Azeb Alghanemi, Awatif Al-Jedani, Ion Mihai
Summary: This paper investigates CRS bi-warped products in contact metric manifolds and proves that there are no proper CRS bi-warped products other than contact CR-biwarped products in Sasakian manifolds. It also provides an important inequality and several applications for CRS bi-warped products in cosymplectic manifolds.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Multidisciplinary Sciences
Ali H. H. Hakami, Mohd Danish Siddiqi, Oguzhan Bahadir, Toukeer Khan
Summary: In this study, the authors investigate quasi-hemi-slant submanifolds in trans-Sasakian manifolds. They provide necessary and sufficient conditions for the integrability of distributions using quasihemi-slant submanifolds. The authors also analyze the geometric properties of foliations dictated by the distributions and discuss the requirements for quasi-hemi-slant factors to be totally geodesic in submanifolds of trans-Sasakian manifolds. Lastly, they illustrate the application of a submanifold with a quasi-hemi-slant factor in number theory.
Article
Mathematics
Cristina E. Hretcanu, Adara M. Blaga
Summary: This paper studies the properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and constructs examples in Euclidean spaces. Additionally, it investigates some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.
Article
Mathematics
Ali H. Alkhaldi, Akram Ali
Summary: This work examines two types of bi-warped product submanifolds in nearly trans-Sasakian manifolds and establishes inequalities for the squared norm of the second fundamental form. The main results presented here extend several previous findings and include applications in mathematical physics and relationships between the second fundamental form and Dirichlet energy. Additionally, the connection between eigenvalues and the second fundamental form is established.
Article
Mathematics
S. S. Shukla, Vipul Singh
Summary: In this paper, the concepts of screen slant and semi-slant lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold are introduced. Examples are provided and characterization theorems for the existence of such lightlike submersions are obtained. The integrability conditions of distributions involved in the definitions of both classes of lightlike submersions are also investigated.
LOBACHEVSKII JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Shiv Sharma Shukla, Akhilesh Yadav
Summary: This paper introduces the concept of screen semi-slant lightlike submanifolds of indefinite Kaehler manifolds, provides characterization theorems and discusses integrability conditions of distributions D-1, D-2 and RadTM on these submanifolds. It also explores necessary and sufficient conditions for totally geodesic foliations determined by certain distributions, as well as mixed geodesic screen semi-slant lightlike submanifolds.
THAI JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Megha Pruthi, Sangeet Kumar
Summary: We introduce the concept of pointwise bi-slant lightlike submanifolds of indefinite almost Hermitian manifolds. A characterization theorem is provided for the existence of such submanifolds, along with a non-trivial example. The integrability conditions for the associated distributions are derived. Additionally, the existence of warped product pointwise bi-slant lightlike submanifolds of indefinite Kaehler manifolds is investigated.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics, Applied
Meraj Ali Khan, Ali H. Alkhaldi, Mohd Aquib
Summary: The study aims to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the alpha-Laplacian operator on Riemannian manifolds. Various methods are used to determine the first eigenvalue for the alpha-Laplacian operator on closed oriented pseudo-slant submanifolds in a generalized Sasakian space form.
