On some Kähler manifolds with Norden metric

We investigate the Kähler manifolds with Norden metric whose curvature tensor can be expressed in the terms of Ricci tensors only and whose holomorphically conformal curvature tensor vanishes.     

On 3-dimensional contact metric manifolds with ▽ξτ=0

We give the classification of the 3-dimensional contact metric manifolds satisfying =0, which they have: harmonic curvature, or -parralel Ricci tensor or cyclic -parallel Ricci tensor.     

Explicit construction of a Chern–Moser connection for CR manifolds of codimension two

In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codimension two, i.e. a pair , consisting of a principal bundle over M and of a Cartan connection form over P, satisfying the following property: the (local) CR transformations are in one to one correspondence with the (local) automorphisms for which . For any , this construction determines an explicit monomorphism of the stability subalgebra Lie (Aut(M)_x) into the Lie algebra of the structure group H of P. Mathematics Subject Classification (2000) Primary 32V05, Secondary 53C15, 53A55     

On transverse Killing fields of metric foliations¶of manifolds with positive curvature

In this paper, we extend a result by H. Takagi on the non-existence of mutually commuting and linearly independent Killing vector fields on positively curved Riemannian manifolds. Further, a kind of “Compact Leaf Theorem” is proved for metric foliations of closed manifolds with positive sectional curvature. Received: 26 May 2000 / Revised version: 28 February 2001     

Compactness theorems and the Calabi flow on Kähler surfaces with stable tangent bundle

Abstract. In this paper, we prove some compactness theorems and collapse phenomenon on compact K?hler surfaces with stable tangent bundle. We then apply the results to the Calabi flow. More precisely, we prove, under suitable curvature conditions, the longtime existence and asymptotic convergence for solutions of the Calabi flow on compact K?hler surfaces admitting no nonzero holomorphic tangent vector fields and with stable tangent bundle. We also give some examples where the Calabi flow blows up. Received January 7, 1999 / Revised February 2, 2000 / Published online July 20, 2000     

On the Chern–Simons–Higgs vortex equation without gauge fields

This paper is concerned with the nonself-dual Chern–Simons–Higgs model on R²${\mathbb{R}}^2$ with vanishing gauge fields. We prove the existence of radial solutions with the topological boundary condition, and the nonexistence of radial solutions with the nontopological boundary condition. We also establish the asymptotic properties of solutions and derive the quantization of the potential energy.     

On the connection between the Hilger and Radon–Nikodym derivatives

We show that the Hilger derivative on time scales is a special case of the Radon–Nikodym derivative with respect to the natural measure associated with every time scale. Moreover, we show that the concept of delta absolute continuity agrees with the one from measure theory in this context.     

Almost contact metric hypersurfaces with type number 0 or 1 in nearly-Kählerian manifolds

It is proved that for an almost contact metric hypersurface in a nearly-Kählerian manifold the condition that the type number is equal to 1 or 0 is not only necessary but also sufficient for this almost contact metric structure be weakly cosymplectic.     

Weil-Petersson metric in the moduli space of compact polarized Kähler-Einstein manifolds of zero first Chern class

We study the problem of computing the curvature of the Weil-Petersson metric of the moduli space of general compact polarized Kähler-Einstein manifolds of zero first Chern class. We use canonical lifting of vector fields from the moduli space to the total deformation space to obtain a formula for the curvature of the Weil-Petersson metric. From this formula we obtain negative bisectional curvature for certain directions. This formula also reprove and explain the recent result of Schumacher that the holomorphic sectional curvature of the Weil-Petersson metric for K3-surfaces and symplectic manifolds are negative.     

On mappings in the Orlicz–Sobolev classes on Riemannian manifolds

We study the problems of the continuous and homeomorphic extension to the boundary of lower Q-homeomorphisms between domains on Riemannian manifolds and formulate the corresponding consequences for homeomorphisms with finite distortion in the Orlicz–Sobolev classes W_loc^1,j W_{loc}^{1,varphi } under a condition of the Calderon type for the function φ and, in particular, in the Sobolev classes W_loc^1,p W_{loc}^{1,p} for p > n − 1.     

On a CR Transversality Problem Through the Approach of the Chern–Moser Theory

In this paper, we give a geometric condition for a CR map, which sends a CR non-umbilical Levi non-degenerate hypersurface in ? ⁿ⁺¹ into the hyperquadric in ? ⁿ⁺² with the same signature, to be CR transversal.     

On a ogawa–type integral with application to the fractional brownian motion

We construct a deterministic Ogawa–type integral with respect to a continuous function that, in particular, can be a trajectory of the Fractional Brownian motion. This integral is related with the Stratonovich integral and with the integrals introduced by Ciesielski et altri and Zähle. We give a sufficient condition for the integrability of a function in this sense, that does not imply its continuity. Under this sufficient condition, we obtain a Besov regularity property of the indefinite integral. We also study the stochastic Ogawa integral for stochastic processes when integrate with respect to the Fractional Brownian motion of Hurst parameter H ∈ (1/2, 1)     

On the Jordan–Kinderlehrer–Otto variational scheme and constrained optimization in the Wasserstein metric

We prove the monotonicity of the second-order moments of the discrete approximations to the heat equation arising from the Jordan–Kinderlehrer–Otto (JKO) variational scheme. This issue appears in the study of constrained optimization in the 2-Wasserstein metric performed by Carlen and Gangbo for the kinetic Fokker–Planck equation. As an alternative to their duality method, we provide the details of a direct approach, via Lagrange multipliers. Estimates for the fourth-order moments in the constrained case, which are essential to the subsequent alternate analysis, are also obtained. Partial support provided by NSF grant DMS 0305794.     

On the Geometry of the （1, 1）-Tensor Bundle with Sasaki Type Metric

Curvature properties are studied for the Sasaki metric on the (1,1) tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-K(a)hler-Nordenian B-metrics are constructed on the (1,1) tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.     

On almost contact metric hypersurfaces with type number 1 in 6-dimensional Kähler submanifolds of the Cayley algebra

We prove that the condition for the type number of an almost contact metric surface in a six-dimensional Kähler submanifold of the Cayley algebra to be 0 or 1 is not only necessary but also sufficient condition for the almost contact metric structure to be cosymplectic.