School of Mathematics Colloquium
Complex Structures on Product of Circle Bundles over Compact Complex Manifolds.
by Mr. Ajay Singh Thakur
Thursday, November 29, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
Description |
Abstract: Let $L_i \rightarrow X_i$ be holomorphic line bundle over compact complex manifold $X_i$, for $i = 1,2$. With respect to any hermitian inner product over $L_i$, we denote the associated circle bundle by $S(L_i)$. The aim of this talk is to describe a family of complex structures on $S(L_1) \times S(L_2)$. As a special case when $X_i$ are projective space $\mathbb P^{n_i}$ and the line bundles are tautological line bundles, Calabi-Eckmann obtained a family of complex structures on the product of odd dimensional spheres, $S^{2n_1 +1} \times S^{2n_2 +1}$. Later Loeb and Nicolau constructed a more general family of complex structures on $S^{2n_1+1} \times S^{2n_2 +1}$. We generalize the Loeb-Nicolau construction to obtain the complex structures on $S(L_1) \times S(L_2)$. These complex manifolds will be non-K\"{a}hler. This is joint work with Prof P.Sankaran. |