Submanifolds in differentiable manifolds endowed with differential-geometric structures VI.CR-submanifolds in a manifold of almost-complex structure

1989 ◽  
Vol 44 (2) ◽  
pp. 123-152
Author(s):  
N. M. Ostianu
Keyword(s):  
Complex Structure ◽  
Almost Complex Structure ◽  
Geometric Structures ◽  
Differentiable Manifolds ◽  
Almost Complex

ALMOST COMPLEX STRUCTURE ON PATH SPACE

2013 ◽  
Vol 10 (03) ◽  
pp. 1220034 ◽  
Author(s):  
PRADIP KUMAR
Keyword(s):  
Complex Manifold ◽  
Smooth Manifold ◽  
Complex Structure ◽  
Path Space ◽  
Almost Complex Structure ◽  
Geometric Structures ◽  
Almost Complex ◽  
Fréchet Manifold ◽  
Frechet Manifold

Let M be a complex manifold and let PM ≔ C∞([0, 1], M) be space of smooth paths over M. We prove that the induced almost complex structure on PM is weak integrable by extending the result of Indranil Biswas and Saikat Chatterjee of [Geometric structures on path spaces, Int. J. Geom. Meth. Mod. Phys.8(7) (2011) 1553–1569]. Further we prove that if M is smooth manifold with corner and N is any complex manifold then induced almost complex structure 𝔍 on Fréchet manifold C∞(M, N) is weak integrable.

scholarly journals On the General Theory of Differentiable Manifolds with Almost Tangent Structure

1965 ◽  
Vol 8 (6) ◽  
pp. 721-748 ◽  
Author(s):  
Hermes A. Eliopoulos
Keyword(s):  
General Theory ◽  
Complex Structure ◽  
Differentiable Manifold ◽  
Linear Operators ◽  
Identity Operator ◽  
Almost Complex Structure ◽  
Differentiable Manifolds ◽  
Almost Complex ◽  
Image Position ◽  
Almost Tangent Structure

Some of the most important G-Structures of the first kind [1] are those defined by linear operators satisfying algebraic relations. If the linear operator J acting on the complexified space of a differentiable manifold V satisfies a relation of the formwhere I is the identity operator, the manifold has an almost complex structure ([2] [3]). The structures defined byare the almost product structures ([3] [4]).

GEOMETRIC STRUCTURES ON PATH SPACES

2011 ◽  
Vol 08 (07) ◽  
pp. 1553-1569 ◽  
Author(s):  
INDRANIL BISWAS ◽  
SAIKAT CHATTERJEE
Keyword(s):  
Complex Structure ◽  
Almost Complex Structure ◽  
Geometric Structures ◽  
Smooth Maps ◽  
Almost Complex

Let M be a C∞ manifold, and let [Formula: see text] be the space of all smooth maps from [0, 1] to M. We investigate geometric structures on [Formula: see text] constructed from the geometric structures on M. In particular, we show that a generalized (almost) complex structure on M produce a generalized (almost) complex structure on [Formula: see text].

The almost complex structure on 𝕊6 and related Schrödinger flows

2018 ◽  
Vol 29 (14) ◽  
pp. 1850099 ◽  
Author(s):  
Qing Ding ◽  
Shiping Zhong
Keyword(s):  
Complex Structure ◽  
Type System ◽  
Text Structure ◽  
Almost Complex Structure ◽  
Nls Equation ◽  
Geometric Properties ◽  
Nonlinear Schrödinger ◽  
Almost Complex ◽  
Complex Functions

In this paper, by using the [Formula: see text]-structure on Im[Formula: see text] from the octonions [Formula: see text], the [Formula: see text]-binormal motion of curves [Formula: see text] in [Formula: see text] associated to the almost complex structure on [Formula: see text] is studied. The motion is proved to be equivalent to Schrödinger flows from [Formula: see text] to [Formula: see text], and also to a nonlinear Schrödinger-type system (NLSS) in three unknown complex functions that generalizes the famous correspondence between the binormal motion of curves in [Formula: see text] and the focusing nonlinear Schrödinger (NLS) equation. Some related geometric properties of the surface [Formula: see text] in Im[Formula: see text] swept by [Formula: see text] are determined.

scholarly journals BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS

2008 ◽  
Vol 17 (11) ◽  
pp. 1429-1454 ◽  
Author(s):  
FRANCESCO COSTANTINO
Keyword(s):  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Homotopy Classes ◽  
Almost Complex Structures ◽  
Almost Complex

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

scholarly journals Coclosed G2-structures inducing nilsolitons

2018 ◽  
Vol 30 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Leonardo Bagaglini ◽  
Marisa Fernández ◽  
Anna Fino
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Nilpotent Lie Algebras ◽  
Almost Complex ◽  
Metric Structures ◽  
Trivial Center ◽  
Nilsoliton Metric

Abstract We show obstructions to the existence of a coclosed {\mathrm{G}_{2}} -structure on a Lie algebra {\mathfrak{g}} of dimension seven with non-trivial center. In particular, we prove that if there exists a Lie algebra epimorphism from {\mathfrak{g}} to a six-dimensional Lie algebra {\mathfrak{h}} , with the kernel contained in the center of {\mathfrak{g}} , then any coclosed {\mathrm{G}_{2}} -structure on {\mathfrak{g}} induces a closed and stable three form on {\mathfrak{h}} that defines an almost complex structure on {\mathfrak{h}} . As a consequence, we obtain a classification of the 2-step nilpotent Lie algebras which carry coclosed {\mathrm{G}_{2}} -structures. We also prove that each one of these Lie algebras has a coclosed {\mathrm{G}_{2}} -structure inducing a nilsoliton metric, but this is not true for 3-step nilpotent Lie algebras with coclosed {\mathrm{G}_{2}} -structures. The existence of contact metric structures is also studied.

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