This book expounds on the recent developments in applications of holomorphic functions in the theory of hypercomplex and anti-Hermitian manifolds as well as in the geometry of bundles. It provides detailed information about holomorphic functions in algebras and discusses some of the areas in geometry with applications. The book proves the existence of a one-to-one correspondence between hyper-complex anti-Kähler manifolds and anti-Hermitian manifolds with holomorphic metrics, and also a deformed lifting to bundles. Researchers and students of geometry, algebra, topology and physics may find the book useful as a self-study guide.

ARIF SALIMOV is Full Professor and Head of the Department Algebra and Geometry, Faculty of Mechanics and Mathematics, Baku State University. An Azerbaijani/Soviet mathematician, honoured scientist of Azerbaijan, he is known for his research in differential geometry. He earned his B.Sc. degree from Baku State University, Azerbaijan, in 1978, a PhD and Doctor of Sciences (Habilitation) degrees in geometry from Kazan State University, Russia, in 1984 and 1998, respectively. His advisor was Vladimir Vishnevskii. He is an author/co-author of more than 100 research papers. His primary areas of research are theory of lifts in tensor bundles, geometrical applications of tensor operators, special Riemannian manifolds, indefinite metrics and general geometric structures on manifolds (almost complex, almost product, hypercomplex, Norden structures, etc.).