160 research outputs found
Slant immersions in -manifolds
Odd-dimensional non anti-invariant slant submanifolds of an α- Kenmotsu manifold are studied. We relate slant immersions into a Kähler manifold with suitable slant submanifolds of an α-Kenmotsu manifold. More generally, in the framework of Chinea-Gonzalez, we specify the type of the almost contact metric structure induced on a slant submanifold, then stating a local classification theorem. The case of austere immersions is discussed. This helps in proving a reduction theorem of the codimension. Finally, slant submanifolds which are generalized Sasakian space-forms are described
Special almost Hermitian geometry
We study the classification of special almost hermitian manifolds in Gray and
Hervella's type classes. We prove that the exterior derivatives of the
symplectic form and the complex volume form contain all the information about
the intrinsic torsion of the \SUn(n)-structure. Furthermore, we apply the
obtained results to almost hyperhermitian geometry. Thus, we show that the
exterior derivatives of the three K{\"a}hler forms of an almost hyperhermitian
manifold are sufficient to determine the three covariant derivatives of such
forms, i.e., the three mentioned exterior derivatives determine the intrinsic
torsion of the {\sl Sp}(n)-structure.Comment: 27 page
Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
For a given complex n-fold M we present an explicit construction of all
complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For
physical applications we consider the case of M being a Calabi-Yau 2-fold. We
show that for such M, there is a subclass of the 3-folds that we construct,
which has natural families of non-Kaehler SU(3)-structures satisfying the
conditions for N = 1 supersymmetry in the heterotic string theory compactified
on the 3-folds. We present examples in the aforementioned subclass with M being
a K3-surface and a 4-torus.Comment: LaTeX, 17 pages, organization of the paper was changed, typos
correcte
Almost Hermitian 6-Manifolds Revisited
A Theorem of Kirichenko states that the torsion 3-form of the characteristic
connection of a nearly K\"ahler manifold is parallel. On the other side, any
almost hermitian manifold of type admits a unique connection
with totally skew symmetric torsion. In dimension six, we generalize
Kirichenko's Theorem and we describe almost hermitian -manifolds
with parallel torsion form. In particular, among them there are only two types
of -manifolds with a non-abelian holonomy group, namely twistor
spaces of 4-dimensional self-dual Einstein manifolds and the invariant
hermitian structure on the Lie group \mathrm{SL}(2, \C). Moreover, we
classify all naturally reductive hermitian -manifolds with small
isotropy group of the characteristic torsion.Comment: 26 pages, revised versio
Curvature decomposition of G_2 manifolds
Explicit formulas for the -components of the Riemannian curvature tensor
on a manifold with a structure are given in terms of Ricci contractions.
We define a conformally invariant Ricci-type tensor that determines the
27-dimensional part of the Weyl tensor and show that its vanishing on compact
manifold with closed fundamental form forces the three-form to be
parallel. A topological obstruction for the existence of a structure with
closed fundamental form is obtained in terms of the integral norms of the
curvature components. We produce integral inequalities for closed
manifold and investigate limiting cases. We make a study of warped products and
cohomogeneity-one manifolds. As a consequence every Fern\'andez-Gray type
of structure whose scalar curvature vanishes may be realized such that
the metric has holonomy contained in .Comment: LaTeX 2e, 26 pages, 2 tables. Changes in version 2: shortened,
reorganized, misprints corrected, several remarks and new introduction. A
formula in the proof of Theorem 1.2a has been corrected. Submitte
Riemannian submersions from almost contact metric manifolds
In this paper we obtain the structure equation of a contact-complex
Riemannian submersion and give some applications of this equation in the study
of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea
The complex Goldberg-Sachs theorem in higher dimensions
We study the geometric properties of holomorphic distributions of totally
null -planes on a -dimensional complex Riemannian manifold
, where and . In
particular, given such a distribution , say, we obtain algebraic
conditions on the Weyl tensor and the Cotton-York tensor which guarrantee the
integrability of , and in odd dimensions, of its orthogonal
complement. These results generalise the Petrov classification of the
(anti-)self-dual part of the complex Weyl tensor, and the complex
Goldberg-Sachs theorem from four to higher dimensions.
Higher-dimensional analogues of the Petrov type D condition are defined, and
we show that these lead to the integrability of up to holomorphic
distributions of totally null -planes. Finally, we adapt these findings to
the category of real smooth pseudo-Riemannian manifolds, commenting notably on
the applications to Hermitian geometry and Robinson (or optical) geometry.Comment: Section 2 partly rewritten: issue regarding self-duality clarified.
Section 5.2 clarified. Some remarks added. Lemma 3.7 (previously 3.7)
corrected. A few mathematical and notational inaccuracies corrected, and
typos and sign mistakes fixed throughout. Some references adde
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