We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikov’s extended deformation theory. We provide a non-trivial example of Hertling-Manin’s weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the context of compact nilmanifolds. The calculation of extended deformation and ...

We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikov’s extended deformation theory. We provide a non-trivial example of Hertling-Manin’s weak Frobenius manifold. In addition, we find that Kodaira surface is its own mirror image. Our computation is done in the context of compact nilmanifolds. The calculation of extended deformation and ...

In this paper,  we introduce the notion of  generalized multivalued  $F$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.

Functors preserving weak pullbacks provide the basis for a rich structure theory of coalgebras. We give an easy to use criterion to check whether a functor preserves weak pullbacks. We apply the characterization to the functor F which associates a set X with the set F(X) of all filters on X. It turns out that this functor preserves weak pullbacks, yet does not preserve weak generalized pullback...