Normal Variations of Invariant Hypersurfaces of Framed Manifolds

1972 ◽  
Vol 15 (4) ◽  
pp. 513-521
Author(s):  
Samuel I. Goldberg
Keyword(s):  
Complex Manifold ◽  
Contact Structure ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Marked Contrast ◽  
Almost Complex Manifold ◽  
Almost Contact Structure ◽  
Almost Complex ◽  
Differentiable Vector ◽  
Real Codimension

A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.

The Tangent Bundle of an Almost Complex Manifold

2001 ◽  
Vol 44 (1) ◽  
pp. 70-79 ◽  
Author(s):  
László Lempert ◽  
Róbert Szőke
Keyword(s):  
Complex Manifold ◽  
Tangent Bundle ◽  
Deformation Theory ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Holomorphic Maps ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Natural Way

AbstractMotivated by deformation theory of holomorphic maps between almost complex manifolds we endow, in a natural way, the tangent bundle of an almost complexmanifold with an almost complex structure. We describe various properties of this structure.

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 COHOMOLOGY OF ALMOST-COMPLEX MANIFOLDS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250019 ◽  
Author(s):  
DANIELE ANGELLA ◽  
ADRIANO TOMASSINI
Keyword(s):  
Complex Structure ◽  
Almost Complex Structure ◽  
Complex Manifolds ◽  
Almost Complex Manifolds ◽  
Dynamical Study ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Kähler Structures ◽  
Foliated Manifolds ◽  
Invent Math

Following [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.36(1) (1976) 225–255] to study the cone of semi-Kähler structures on a compact semi-Kähler manifold.

scholarly journals TOTAL REALITY OF CONORMAL BUNDLES OF HYPERSURFACES IN ALMOST COMPLEX MANIFOLDS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1255-1262 ◽  
Author(s):  
ANDREA SPIRO
Keyword(s):  
Complex Structure ◽  
Almost Complex Structure ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Conormal Bundle ◽  
Almost Complex ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real ◽  
Pseudoconvex Hypersurface

A generalization to the almost complex setting of a well-known result by Webster is given. Namely, we prove that if Γ is a strongly pseudoconvex hypersurface in an almost complex manifold (M, J), then the conormal bundle of Γ is a totally real submanifold of (T* M, 𝕁), where 𝕁 is the lifted almost complex structure on T* M defined by Ishihara and Yano.

On an Almost Complex Manifold Approach to Elementary Particles

1977 ◽  
Vol 32 (11) ◽  
pp. 1215-1221
Author(s):  
Julian Ławrynowicz ◽  
Leszek Wojtczak
Keyword(s):  
Complex Manifold ◽  
Nuclear Reactions ◽  
Main Idea ◽  
Elementary Particles ◽  
Fibre Bundles ◽  
Almost Complex Manifold ◽  
Minkowski Space Time ◽  
Almost Complex ◽  
Principal Fibre ◽  
Principal Fibre Bundles

Abstract An almost complex manifold description of elementary particles is proposed which links the approaches given independently by J. Ławrynowicz and L. Wojtczak, and by C. von Westenholz. This description leads to relations between the curvature form of an almost complex manifold, which accounts for the symmetry classification schemes within the frame of principal fibre bundles, and a curved Minkowski space-time via induced smooth mappings characterizing nuclear reactions of type N+π⇄N, where N is some nucleon and π the virtual π-meson of this reaction. Both approaches follow the same main idea of D. A. Wheeler developed in a different way by A.D. Sakharov.

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 On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action

2017 ◽  
Vol 19 (04) ◽  
pp. 1750043 ◽  
Author(s):  
Silvia Sabatini
Keyword(s):  
Fixed Points ◽  
Complex Manifold ◽  
Index Formula ◽  
Circle Action ◽  
Hilbert Polynomial ◽  
Dimensional Manifold ◽  
Hamiltonian Action ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Chern Numbers

Let [Formula: see text] be a compact, connected, almost complex manifold of dimension [Formula: see text] endowed with a [Formula: see text]-preserving circle action with isolated fixed points. In this paper, we analyze the “geography problem” for such manifolds, deriving equations relating the Chern numbers to the index [Formula: see text] of [Formula: see text]. We study the symmetries and zeros of the Hilbert polynomial, which imply many rigidity results for the Chern numbers when [Formula: see text]. We apply these results to the category of compact, connected symplectic manifolds. A long-standing question posed by McDuff and Salamon asked about the existence of non-Hamiltonian actions with isolated fixed points. This question was answered recently by Tolman, with an explicit construction of a 6-dimensional manifold with such an action. One issue that this raises is whether one can find topological criteria that ensure the manifold can only support a Hamiltonian or only a non-Hamiltonian action. In this vein, we are able to deduce such criteria from our rigidity theorems in terms of relatively few Chern numbers, depending on the index. Another consequence is that, if the action is Hamiltonian, the minimal Chern number coincides with the index and is at most [Formula: see text].

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