Curvature on holomorphic plane curves. II
Differential geometry of quaternionic manifolds
Einstein-Hermitian and anti-Hermitian 4-manifolds
We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.
Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind
In this paper we define generalized Kählerian spaces of the first kind given by (2.1)–(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ( and ) and for them we find invariant geometric objects.
Erratum : “Closed transverse -forms on compact complex manifolds”
Estimate of the Einstein-Kähler metric on a weakly pseudoconvex domain in ... .
Existence of Holomorphic Functions on Almost Complex Manifolds.
Geodesic mapping onto Kählerian spaces of the first kind
In the present paper a generalized Kählerian space of the first kind is considered as a generalized Riemannian space with almost complex structure that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives...
Geodesics and circles on real hypersurfaces of type and in a complex space form.
Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.
Higher order contact of real curves in a real hyperquadric. II
Let be an Hermitian quadratic form, of maximal rank and index , defined over a complex vector space . Consider the real hyperquadric defined in the complex projective space by Let be the subgroup of the special linear group which leaves invariant and the distribution defined by the Cauchy Riemann structure induced over . We study the real regular curves of constant type in , tangent to , finding a complete system of analytic invariants for two curves to be locally equivalent...
Holomorphically projective curvature tensors
Holomorphically projective mappings of compact semisymmetric manifolds
In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces onto (pseudo-) Kählerian spaces . We proved that in this case space is holomorphically projective flat and is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian...
Holomorphy angles and sectional curvature in Hermitian elliptic planes over fields and tensor products of fields.
Hyper-Lie Poisson structures
Indefinite Kähler Manifolds.
Instrinsic Connections for Levi Metrics.
Invariant connections and invariant holomorphic bundles on homogeneous manifolds
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when...
Invariant operators on real and complex manifolds.
Isotropic Immersions of Complex Space Forms into Real Space Forms and Mean Curvatures
Using an inequality related to the mean curvature, we give a sufficient condition for an isotropic immersion of a complex space form into a real space form to be parallel.