Results 51 to 60 of about 441,387 (187)

CR STATISTICAL SUBMANIFOLDS [PDF]

The non-existence of CR submanifolds of maximal CR dimension with umbilical shape operator in holomorphic statistical manifolds is proven. Our results are a generalization of the known results in the theory of CR submanifolds in complex space forms ...
Milijević, Mirjana
core   +1 more source

Semi-invariant submanifolds of (g, F)-manifolds [PDF]

Surveys in Mathematics and its Applications, 2010
We introduce (g,F)-manifolds and initiate a study of their semi-invariant submanifolds. These submanifolds are generalizations of CR-submanifolds of Kaehler manifolds.
Novac-Claudiu Chiriac
doaj  

On totally umbilical CR-submanifolds of a Kaehler manifold

International Journal of Mathematics and Mathematical Sciences, 1993
Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or ...
M. A. Bashir
doaj   +1 more source

Vanishing Homology of Warped Product Submanifolds in Complex Space Forms and Applications

Mathematics, 2022
In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold Mn of a complex space form M˜(4ϵ) under extrinsic conditions which involve the Laplacian, the squared norm gradient ...
Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Izhar Ahmad, Akram Ali   +3 more
doaj   +1 more source

Harmonic maps to the circle with higher dimensional singular set

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract In a closed, oriented ambient manifold (Mn,g)$(M^n,g)$ we consider the problem of finding S1$\mathbb {S}^1$‐valued harmonic maps with prescribed singular set. We show that the boundary of any oriented (n−1)$(n-1)$‐submanifold can be realised as the singular set of an S1$\mathbb {S}^1$‐valued map, which is classically harmonic away from the ...
Marco Badran
wiley   +1 more source

CR submanifolds in Kaehler and nearly Kaehler manifolds [PDF]

, 2004
A review of the study of CR, submanifolds within Kaehler and nearly Kaehler manifolds, and the properties of such manifolds with respect submanifold theory in differential geometry.
Gregg, Matthew Thomas
core  

Submanifolds with curvature normals of constant length and the Gauss map [PDF]

, 2004
We show that a submanifold with curvature normal of constant length has constant principal curvatures under suitable global hypothesis.
A. J. Di Scala, C. Olmos, Di Scala, Antonio Jose', Carlos Olmos   +3 more
core   +1 more source

Classification of Four-Dimensional CR Submanifolds of the Homogenous Nearly Kähler ${\mathbb{S}}^{\mathbf{3}}\mathbf{\times }{\mathbb{S}}^{\mathbf{3}}$ Which Almost Complex Distribution Is Almost Product Orthogonal on Itself

Mathematics
The product manifold S3×S3, which belongs to the homogenous six-dimensional nearly Kähler manifolds, admits two structures, the almost complex structure J and the almost product structure P.
Nataša Djurdjević
doaj   +1 more source

Chen optimal inequalities of CR-warped products of generalized Sasakian space form

Journal of Taibah University for Science, 2020
Our main objective of this paper is to derive the relationship between the main extrinsic invariant, and the contact CR δ-invariant (new intrinsic invariant) on a generic submanifold in trans-Sasakian generalized Sasakian space forms.
Aliya Naaz Siddiqui, Akram Ali, Ali H. Alkhaldi   +2 more
doaj   +1 more source

On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

Mathematics, 2021
In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Ωn=NTl×fNϕk in a complex projective space CP2m(4).
Yanlin Li, Ali H. Alkhaldi, Akram Ali, Pişcoran Laurian-Ioan   +3 more
doaj   +1 more source