On holomorphically subprojective kählerian manifold, I

1977 ◽  
Vol 112 (1) ◽  
pp. 217-229 ◽  
Author(s):  
Seiichi Yamaguchi ◽  
Tyuzi Adati
Keyword(s):  
Kählerian Manifold

scholarly journals Three theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra

2003 ◽  
Vol 2003 (47) ◽  
pp. 3015-3022
Author(s):  
Ahmad Al-Othman ◽  
M. Banaru
Keyword(s):  
Minimal Submanifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Cayley Algebra ◽  
Necessary And Sufficient ◽  
Kählerian Manifold

It is proved that cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the octave algebra are ruled manifolds. A necessary and sufficient condition for a cosymplectic hypersurface of a Hermitian submanifoldM6⊂Oto be a minimal submanifold ofM6is established. It is also proved that a six-dimensional Hermitian submanifoldM6⊂Osatisfying theg-cosymplectic hypersurfaces axiom is a Kählerian manifold.

On nonexistence of Kenmotsu structure on аст-hypersurfaces of cosymplectic type of a Kählerian manifold

2019 ◽  
pp. 23-28
Author(s):  
G. Banaru
Keyword(s):  
Hermitian Manifold ◽  
Structural Equations ◽  
Type I ◽  
Almost Hermitian Manifold ◽  
Almost Contact Metric Structure ◽  
Almost Contact Metric ◽  
Contact Metric Structure ◽  
Metric Structures ◽  
Kählerian Manifold ◽  
Almost Contact Metric Structures

Almost contact metric (аст-)structures induced on oriented hypersurfaces of a Kählerian manifold are considered in the case when these аст- structures are of cosymplectic type, i. e. the contact form of these structures is closed. As it is known, the Kenmotsu structure is the most important non-trivial example of an almost contact metric structure of cosymplectic type. The Cartan structural equations of the almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold are obtained. It is proved that an almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold of dimension at least six cannot be a Kenmotsu structure. Moreover, it follows that oriented hypersurfaces of a Kählerian manifold of dimension at least six do not admit non-trivial almost contact metric structures of cosymplectic type that belong to any well studied class of аст-structures. The present results generalize some results on almost contact metric structures on hypersurfaces of an almost Hermitian manifold obtained earlier by V. F. Kirichenko, L. V. Stepanova, A. Abu-Saleem, M. B. Banaru and others.

SCALAR FIELD THEORY ON A KÄHLER MANIFOLD

1989 ◽  
Vol 04 (12) ◽  
pp. 1127-1134
Author(s):  
K.M. COSTA
Keyword(s):  
Scalar Field ◽  
Kernel Methods ◽  
Background Field ◽  
Field Theories ◽  
Coset Space ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Polynomial Complex ◽  
Loop Counter ◽  
Kählerian Manifold

The invariant one-loop counter terms for a class of non-polynomial complex scalar field theories are found using the background field geodesic expansion together with heat kernel methods. These theories have dynamics invariant under a group G with fields that transform linearly only under a subgroup H of G. The fields are coordinates on a complex Kählerian manifold corresponding to the coset space G/H. The technique is applied to the CP n model.

scholarly journals Harmonic Maps and Stability onf-Kenmotsu Manifolds

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Vittorio Mangione
Keyword(s):  
Harmonic Maps ◽  
Riemannian Submersions ◽  
Kenmotsu Manifold ◽  
Holomorphic Map ◽  
Kenmotsu Manifolds ◽  
The Stability ◽  
Kählerian Manifold

The purpose of this paper is to study some submanifolds and Riemannian submersions on anf-Kenmotsu manifold. The stability of aϕ-holomorphic map from a compactf-Kenmotsu manifold to a Kählerian manifold is proven.

scholarly journals Skew-symmetric vector fields on aCR-submanifold of a para-Kählerian manifold

2004 ◽  
Vol 2004 (10) ◽  
pp. 535-540
Author(s):  
Adela Mihai ◽  
Radu Rosca
Keyword(s):  
Vector Field ◽  
Symplectic Form ◽  
Vector Fields ◽  
Geometric Properties ◽  
Infinitesimal Automorphism ◽  
Kählerian Manifold

We deal with aCR-submanifoldMof a para-Kählerian manifoldM˜, which carries aJ-skew-symmetric vector fieldX. It is shown thatXdefines a global Hamiltonian of the symplectic formΩonM⊤andJXis a relative infinitesimal automorphism ofΩ. Other geometric properties are given.

scholarly journals Pseudo-analytic vectors on pseudo-Kählerian manifold

1955 ◽  
Vol 5 (6) ◽  
pp. 987-993 ◽  
Author(s):  
Shigeo Sasaki ◽  
Kentaro Yano
Keyword(s):  
Kählerian Manifold

scholarly journals FAMILIES OF HOLOMORPHIC BUNDLES

2008 ◽  
Vol 10 (04) ◽  
pp. 523-551 ◽  
Author(s):  
ANDREI TELEMAN
Keyword(s):  
Extension Theorem ◽  
Topological Invariant ◽  
Hermitian Metrics ◽  
Yang Mills ◽  
The Family ◽  
Closed Positive Current ◽  
Stable Family ◽  
Holomorphic Bundles ◽  
Algebraic Manifolds ◽  
Kählerian Manifold

The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds. For instance, we prove that stability and semi-stability are Zariski open properties in families when the Gauduchon degree map is a topological invariant, or when the parameter manifold is compact. Second, we show that, for a generically stable family of bundles over a Kähler manifold, the Petersson–Weil form extends as a closed positive current on the whole parameter space of the family. This extension theorem uses classical tools from Yang–Mills theory (e.g., the Donaldson functional on the space of Hermitian metrics and its properties). We apply these results to study families of bundles over a Kählerian manifold Y parametrized by a non-Kählerian surface X, proving that such families must satisfy very restrictive conditions. These results play an important role in our program to prove existence of curves on class VII surfaces [22–24].

Holomorphic sectional curvatures of indefinite complex Grassmann manifolds

1983 ◽  
Vol 93 (1) ◽  
pp. 121-125
Author(s):  
Sebastian Montiel ◽  
Alfonso Romero
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Point Of View ◽  
Holomorphic Sectional Curvature ◽  
Complex Dimension ◽  
Sectional Curvatures ◽  
Bounded Below ◽  
Kählerian Manifolds ◽  
Kählerian Manifold

In (2), indefinite Kählerian manifolds have been examined from the point of view of holomorphic sectional curvature. Examples in (2) show that the analogue of Kulkarni's theorem (see (4), p. 173) for the holomorphic sectional curvature is false and the best possible result in the direction is:Theorem 1 (known, (2)). Let M be a connected indefinite Kählerian manifold with complex dimension n ≥ 2. If the holomorphic sectional curvature of M is bounded above and bounded below, then M is an indefinite complex space form.

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