The Euler number of hyper-K¨ahler manifolds of OG10 type

K Ahler Parabolicty and the Euler Number of Compact Manifolds of Non-positive Sectional Curvature

Let M 2n be a compact Riemannian manifold of non-positive sectional curvature. It is shown that if M 2n is homeomorphic to a KK ahler manifold, then its Euler number satisses the inequality (?1) n (M 2n) 0. Introduction The results of this paper are related to a well-known problem, attributed sometimes to Hopf and sometimes to Chern, to the eeect that the Euler number (M 2n) of a compact Rieman...

Hyper - K ahler

A twistor construction of the hierarchy associated with the hyper-KK ahler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The recursion operator R is constructed and used to build an innnite-dimensional symmetry algebra and in particular higher ows for the hyper-KK ahler equations. It is shown that R acts on the twistor data by multipli...

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Connections and K Ahler Manifolds 3

Twistor Forms on K Ahler Manifolds

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to Hamiltonian 2...