Results 71 to 80 of about 441,387 (187)

Geometry of CR-Submanifolds [PDF]

, 2009
To study the geometry of a manifold, it is more convenient to first embed into a known manifold and then study its geometry. This approach gave impetus to study of submanifold which later developed into an independent and fascinating topic of study.
Kaur, Manjot
core  

Codimension reduction and second fundamental form of CR submanifolds in complex space forms [PDF]

, 2009
Considering n-dimensional real submanifolds M of a complex space form (M¯n+p,g¯,J) which are CR submanifolds of CR dimension n−m2, we study the condition h(FX,Y)+h(X,FY)=0 on the structure tensor F naturally induced from the almost complex structure J of
Djorić, Mirjana
core   +1 more source

Floer theory for the variation operator of an isolated singularity

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae, Cheol‐Hyun Cho, Dongwook Choa, Wonbo Jeong   +3 more
wiley   +1 more source

Radiation therapy response prediction for head and neck cancer using multimodal imaging and multiview dynamic graph autoencoder feature selection

Medical Physics, Volume 52, Issue 10, October 2025.
Abstract Background External beam radiation therapy is a common treatment for head and neck (H&N) cancers. Radiomic features derived from biomedical images have shown promise as effective biomarkers used to assess tumor heterogeneity and predict response to treatment.
Amir Moslemi, Laurentius Oscar Osapoetra, Aryan Safakish, Lakshmanan Sannachi, David Alberico, Gregory J Czarnota   +5 more
wiley   +1 more source

On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

Demonstratio Mathematica, 2014
After brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold.
Gogna Manish, Kumar Rakesh, Nagaich R. K.   +2 more
doaj   +1 more source

Global eigenfamilies on closed manifolds

Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.
Abstract We study globally defined (λ,μ)$(\lambda,\mu)$‐eigenfamilies on closed Riemannian manifolds. Among others, we provide (non‐)existence results for such eigenfamilies, examine topological consequences of the existence of eigenfamilies and classify (λ,μ)$(\lambda,\mu)$‐eigenfamilies on flat tori. It is further shown that for f=f1+if2$f=f_1+i f_2$
Oskar Riedler, Anna Siffert
wiley   +1 more source

Minimal $CR$ submanifolds of complex space forms [PDF]

, 1987
Integral formulas for the second fundamental form of submanifolds immersed in a complex space form are given. As applications, pinching theorems for compact minimal $CR$ submanifolds with flat normal connection immersed in a complex projective space are ...
Kon, Masahiro
core  

Geometric Inequalities for Skew CR-Warped Product Submanifolds in Locally Conformal Almost Cosymplectic Manifolds

Mathematics
In this paper, we investigate contact skew CR-warped product submanifolds of locally conformal almost cosymplectic manifolds, a framework that simultaneously generalizes warped product pseudo-slant, semi-slant, and contact CR-submanifolds.
Ali H. Alkhaldi, Fatemah Mofarreh, Huda M. Alshanbari, Akram Ali   +3 more
doaj   +1 more source

CR$CR$ analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract Using iterated uniform local completion, we introduce a notion of continuous CR$CR$ functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and CR$CR$ functions on CR$CR$ submanifolds. Under additional assumptions of set‐theoretical weak pseudo‐concavity, we prove optimal maximum modulus ...
Mauro Nacinovich, Egmont Porten
wiley   +1 more source

Nondensity results in high‐dimensional stable Hamiltonian topology

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not C3$C^3$‐dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension 2n⩾8$2n\geqslant 8$.
Robert Cardona, Fabio Gironella
wiley   +1 more source