Toward a Generalized Gauss-Bonnet Formula for Complete, Open Manifolds
Trace decomposition and recurrency
Transversally symmetric immersions
We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.
TT-tensors and conformally flat structures on 3-manifolds
We study TT-tensors on conformally flat 3-manifolds (M,g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when M is simply connected and has vanishing 2nd de Rham cohomology.
Twisteurs et applications harmoniques en dimension 4
Twistor Holomorphic Immersions of Real Surfaces Into Kähler Surface.
Two applications of an integral formula
Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature
In this paper, we prove two generalized versions of the Cheeger-Gromoll splitting theorem via the non-negativity of the Bakry-Émery Ricci curavture on complete Riemannian manifolds.
Un panorama de variedades aproximadamente Kähler.
Un théorème de prolongement spinoriel
Una classe di varietà quaternionali che ammettono una struttura complessa compatibile
Si dimostra l'esistenza di una struttura complessa compatibile globale sulle varietà quaternionali di Hermite-Weyl compatte regolari. Se ne deducono alcune restrizioni sui numeri di Betti.
Uniqueness of Kähler-Einstein cone metrics.
The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.
Unit tangent sphere bundles with constant scalar curvature
As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
Warped Product CR-Submanifolds of Lorentzian -Kenmotsu Manifolds
Warped Product Semi-Slant Submanifolds of a Sasakian Manifold
2000 Mathematics Subject Classification: 53C40, 53C25.In the present note, it is proved that there donot exist warped product semi-slant submanifolds in a Sasakian manifold other than contact CR-warped product submanifolds and thus the results obtained in [8] are generalized.
Warped product submanifolds in quaternion.
Weakly -symmetric contact metric spaces.
Weakly-Einstein hermitian surfaces
A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as -Einstein condition we obtain a complete classification of the compact locally homogeneous -Einstein Hermitian surfaces. We also provide large families of non-homogeneous -Einstein (but non-Einstein) Hermitian metrics on , , and on the product surface of two curves and whose genuses are greater...
Weighted minimal translation surfaces in the Galilean space with density
Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify such a surface with vanishing weighted mean curvature.
Weil-Petersson Metric in the Moduli Space of Compact Polarized Kähler-Einstein Manifolds of Zero First Chern Class.