Results 11 to 20 of about 937 (72)

Canonical complex extensions of Kähler manifolds

Journal of the London Mathematical Society, Volume 101, Issue 2, Page 786-827, April 2020., 2020
Abstract Given a complex manifold X, any Kähler class defines an affine bundle over X, and any Kähler form in the given class defines a totally real embedding of X into this affine bundle. We formulate conditions under which the affine bundles arising this way are Stein and relate this question to other natural positivity conditions on the tangent ...
Daniel Greb, Michael Lennox Wong
wiley   +1 more source

A remark on four‐dimensional almost Kähler‐Einstein manifolds with negative scalar curvature

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 35, Page 1837-1842, 2004., 2004
Concerning the Goldberg conjecture, we will prove a result obtained by applying the result of Iton in terms of L2‐norm of the scalar curvature.
R. S. Lemence, T. Oguro, K. Sekigawa
wiley   +1 more source

A Kähler Einstein structure on the tangent bundle of a space form

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 3, Page 183-195, 2001., 2001
We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive ...
Vasile Oproiu
wiley   +1 more source

Totally real submanifolds in a complex projective space

International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 205-208, 1999., 1999
In this paper, we establish the following result: Let M be an n‐dimensional complete totally real minimal submanifold immersed in CPn with Ricci curvature bounded from below. Then either M is totally geodesic or inf r ≤ (3n + 1)(n − 2)/3, where r is the scalar curvature of M.
Liu Ximin
wiley   +1 more source

Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics

Complex Manifolds, 2017
We report on a question, posed by L. Ornea and M. Verbitsky in [32], about examples of compact locally conformal symplectic manifolds without locally conformal Kähler metrics.
Bazzoni Giovanni, Marrero Juan Carlos
doaj   +1 more source

Deformation classes in generalized Kähler geometry

Complex Manifolds, 2020
We describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry.
Gibson Matthew, Streets Jeffrey
doaj   +1 more source

On some compact almost Kähler locally symmetric space

International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 69-72, 1998., 1997
In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric space M is a weakly ,∗‐Einstein vnanifold with non‐negative ,∗‐scalar curvature, then M is a Kähler manifold.
Takashi Oguro
wiley   +1 more source

Stenzel's Ricci-flat Kaehler metrics are not projectively induced [PDF]

, 2020
We investigate the existence of a holomorphic and isometric immersion in the complex projective space for the complete Ricci-flat Kaehler metrics constructed by M. B.
Zedda, Michela
core   +1 more source

On CR‐submanifolds of the six‐dimensional sphere

International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 201-203, 1995., 1995
We consider proper CR‐submanifolds of the six‐dimensional sphere S6. We prove that S6 does not admit compact proper CR‐submanifolds with non‐negative sectional curvature and integrable holomorphic distribution.
M. A. Bashir
wiley   +1 more source

Kähler-Einstein metrics: Old and New

Complex Manifolds, 2017
We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability).
Angella Daniele, Spotti Cristiano
doaj   +1 more source