Some notes on metallic Kähler manifolds

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

Complex Hessian Equations on Some Compact Kähler Manifolds

On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f : M → R and an integer 1 < k < m, we want to solve uniquely in ω the equation ω̃ ∧ωm−k eω, relying on the notion of k-positivity for ω̃ ∈ ω the extreme cases are solved: k m by Yau in 1978 , and k 1 trivially . We solve by the continuity method the corresponding complex elliptic kthHessian equation...

0 Ricci flow on Kähler manifolds

Ricci Flow on Kähler-einstein Manifolds

On some generalized recurrent manifolds

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...