1. CMB Online first
||Generalized Goldberg Formula|
In this paper we prove a useful formula for the graded commutator
of the Hodge
codifferential with the left wedge multiplication by a fixed
$p$-form acting on
the de Rham algebra of a Riemannian manifold. Our formula generalizes
stated by Samuel I. Goldberg for the case of 1-forms. As first
application we obtain new identities on locally conformally KÃ¤hler
and quasi-Sasakian manifolds. Moreover, we prove that under suitable
a certain subalgebra of differential forms in a compact manifold
is quasi-isomorphic as a CDGA to the full de Rham algebra.
Keywords:graded commutator, Hodge codifferential, Hodge laplacian, de Rham cohomology, locally conformal Kaehler manifold, quasi-Sasakian manifold
2. CMB 2013 (vol 57 pp. 401)
||Curvature of $K$-contact Semi-Riemannian Manifolds|
In this paper we characterize $K$-contact semi-Riemannian manifolds
and Sasakian semi-Riemannian manifolds in terms of
curvature. Moreover, we show that any conformally flat $K$-contact
semi-Riemannian manifold is Sasakian and of constant sectional
curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes
the causal character of the Reeb vector field. Finally, we give some
results about the curvature of a $K$-contact Lorentzian manifold.
Keywords:contact semi-Riemannian structures, $K$-contact structures, conformally flat manifolds, Einstein Lorentzian-Sasaki manifolds
Categories:53C50, 53C25, 53B30
3. CMB 2009 (vol 53 pp. 206)
||Semi-Slant Submanifolds of an Almost Paracontact Metric Manifold|
In this paper, we define and study the geometry of semi-slant submanifolds of an almost paracontact metric manifold. We give some characterizations for a submanifold to be semi-slant submanifold to be semi-slant product and obtain integrability conditions for the distributions involved in the definition of a semi-slant submanifold.
Keywords:paracontact metric manifold, slant distribution, semi-slant submanifold, semi-slant product
Categories:53C15, 53C25, 53C40
4. CMB 2008 (vol 51 pp. 359)
||Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator |
Real hypersurfaces in a complex space form whose structure
Jacobi operator is symmetric along the Reeb flow are studied. Among
them, homogeneous real hypersurfaces of type $(A)$ in a complex
projective or hyperbolic space are characterized as those whose structure
Jacobi operator commutes with the shape operator.
Keywords:complex space form, real hypersurface, structure Jacobi operator
Categories:53B20, 53C15, 53C25
5. CMB 2000 (vol 43 pp. 440)
||On the Existence of a New Class of Contact Metric Manifolds |
A new class of 3-dimensional contact metric manifolds is found.
Moreover it is proved that there are no such manifolds in
dimensions greater than 3.
Keywords:contact metric manifolds, generalized $(\kappa,\mu)$-contact metric manifolds