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 Totally Real Submanifolds in a 6-Sphere

1990 ◽  
Vol 33 (2) ◽  
pp. 162-166
Author(s):  
M. A. Bashir
Keyword(s):  
Complex Structure ◽  
Dimensional Sphere ◽  
Almost Complex Structure ◽  
Real Submanifolds ◽  
Cayley Algebra ◽  
Almost Complex ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real ◽  
Kaehlerian Manifold

AbstractThe 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. With respect to this structure S6 is a nearly Kaehlerian manifold. We investigate 2-dimensional totally real submanifolds in S6. We prove that a 2-dimensional totally real submanifold in S6 is flat.

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.

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.

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.

scholarly journals TOTALLY REAL SURFACES IN $S^6$

2021 ◽  
Vol 23 (1) ◽  
pp. 11-14
Author(s):  
SHARIEF DESHMUKH
Keyword(s):  
Gaussian Curvature ◽  
Complex Structure ◽  
Second Fundamental Form ◽  
Real Surface ◽  
Almost Complex Structure ◽  
Constant Gaussian Curvature ◽  
Totally Geodesic ◽  
The Second Fundamental Form ◽  
Almost Complex ◽  
Totally Real

The normal bundle $\bar \nu$ of a totally real surface $M$ in $S^6$ splits as $\bar\nu= JTM\oplus \bar\mu$ where $TM$ is the tangent bundle of $M$ and  $\bar\mu$ is sub­bundle of $\bar\nu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) \in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic).

scholarly journals On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

2021 ◽  
pp. 2150075
Author(s):  
Andrea Cattaneo ◽  
Antonella Nannicini ◽  
Adriano Tomassini
Keyword(s):  
Complex Structure ◽  
Kodaira Dimension ◽  
Classification Theory ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Almost Complex Manifolds ◽  
Kähler Structure ◽  
Almost Complex Structures ◽  
Almost Complex ◽  
Almost Kähler

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact [Formula: see text]-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text]. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

scholarly journals Remarks on a totally real submanifold

1975 ◽  
Vol 51 (1) ◽  
pp. 5-6 ◽  
Author(s):  
Seiichi Yamaguchi ◽  
Toshihiko Ikawa
Keyword(s):  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

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.

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