scholarly journals Tangent Dirac Structures and Poisson Dirac Submanifolds

2015 ◽  
Vol 62 (1) ◽  
pp. 21-24
Author(s):  
Md Showkat Ali ◽  
MG M Talukder ◽  
MR Khan
Keyword(s):  
Fixed Point ◽  
Poisson Structure ◽  
Normal Bundle ◽  
Dirac Structure ◽  
Fixed Point Set ◽  
Dirac Structures ◽  
Coisotropic Submanifold ◽  
Point Set

The local equations that characterize the submanifolds N of a Dirac manifold M is an isotropic (coisotropic) submanifold of TM endowed with the tangent Dirac structure. In the Poisson case which is a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In this paper we have proved a theorem in the general Poisson case that the fixed point set MG has a natural induced Poisson structure that implies a Poisson-Dirac submanifolds, where G×M?M be a proper Poisson action. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21955 Dhaka Univ. J. Sci. 62(1): 21-24, 2014 (January)

scholarly journals TANGENT DIRAC STRUCTURES AND SUBMANIFOLDS

2005 ◽  
Vol 02 (05) ◽  
pp. 759-775 ◽  
Author(s):  
IZU VAISMAN
Keyword(s):  
Poisson Structure ◽  
Normal Bundle ◽  
Dirac Structure ◽  
Dirac Structures ◽  
Isotropic Submanifold ◽  
Coisotropic Submanifold ◽  
Definition Of ◽  
Simple Definition ◽  
The Way

We write down the local equations that characterize the submanifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of TM endowed with the tangent Dirac structure. In the Poisson case, these formulas once again prove a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In the presymplectic case it is the isotropy of the normal bundle which characterizes the corresponding notion of a Dirac submanifold. On the way, we give a simple definition of the tangent Dirac structure, make new remarks about it and establish its characteristic, local formulas for various interesting classes of submanifolds of a Dirac manifold.

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

Rational Integer Invariants of Regular Cyclic Actions

2004 ◽  
Vol 47 (1) ◽  
pp. 60-72 ◽  
Author(s):  
Robert D. Little
Keyword(s):  
Fixed Point ◽  
Normal Bundle ◽  
Complex Structure ◽  
Rational Integer ◽  
Fixed Point Set ◽  
Cyclic Action ◽  
Point Set ◽  
Smooth Map

AbstractLet g : M2n → M2n be a smooth map of period m ≥ 2 which preserves orientation. Suppose that the cyclic action defined by g is regular and that the normal bundle of the fixed point set F has a g-equivariant complex structure. Let F ⋔ F be the transverse self-intersection of F with itself. If the g-signature Sign(g, M) is a rational integer and n < ϕ(m), then there exists a choice of orientations such that Sign(g, M) = Sign F = Sign(F ⋔ F).

scholarly journals BOUNDS ON THE DIMENSION OF MANIFOLDS WITH INVOLUTION FIXING Fn ∪ F2

2008 ◽  
Vol 50 (3) ◽  
pp. 595-604 ◽  
Author(s):  
PEDRO L. Q. PERGHER ◽  
FÁBIO G. FIGUEIRA
Keyword(s):  
Fixed Point ◽  
Upper Bound ◽  
Normal Bundle ◽  
Smooth Manifold ◽  
Upper Bounds ◽  
Fixed Point Set ◽  
Similar Question ◽  
Cobordism Class ◽  
Point Set

AbstractLet Mm be a closed smooth manifold with an involution having fixed point set of the form Fn ∪ F2, where Fn and F2 are submanifolds with dimensions n and 2, respectively, where n ≥ 4 is even (n < m). Suppose that the normal bundle of F2 in Mm, μ → F2, does not bound, and denote by β the stable cobordism class of μ → F2. In this paper, we determine the upper bound for m in terms of the pair (n, β) for many such pairs. The similar question for n odd (n ≥ 3) was completely solved in a previous paper of the authors. The existence of these upper bounds is guaranteed by the famous 5/2-theorem of Boardman, which establishes that, under the above hypotheses, m ≤ 5/2n.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

scholarly journals On soft quasi-pseudometric spaces

2021 ◽  
Vol 22 (1) ◽  
pp. 17
Author(s):  
Hope Sabao ◽  
Olivier Olela Otafudu
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Soft Set ◽  
Fixed Point Set ◽  
Point Set ◽  
The Absolute ◽  
Pseudometric Space

<p>In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every soft quasi-pseudometric induces a compatible quasi-pseudometric on the collection of all soft points of the absolute soft set whenever the parameter set is finite. We then introduce the concept of soft Isbell convexity and show that a self non-expansive map of a soft quasi-metric space has a nonempty soft Isbell convex fixed point set.</p>

scholarly journals Finite groups acting on hyperelliptic 3-manifolds

2020 ◽  
Vol 29 (04) ◽  
pp. 2050021
Author(s):  
Mattia Mecchia
Keyword(s):  
Fixed Point ◽  
Simple Group ◽  
Finite Groups ◽  
Prime Power ◽  
Simple Groups ◽  
Fixed Point Set ◽  
Point Set

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to [Formula: see text] Such involutions are called hyperelliptic as the manifolds admitting such an action. We consider finite groups acting on 3-manifolds and containing hyperelliptic involutions whose fixed-point set has [Formula: see text] components. In particular we prove that a simple group containing such an involution is isomorphic to [Formula: see text] for some odd prime power [Formula: see text], or to one of four other small simple groups.

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