Differential Geometry Of Complex Manifold

Development of Mathematics is under process since last many centuries and in last few centuries, new branches of Mathematics have been developed by Mathematicians. Gauss laid down the foundation of Differential Geometry of surface in three-dimensional Euclidean space in early nineteenth century. Riemann (1854) introduced the concept of differential Geometry for a space of dimension more than 3. New concepts like Beltrami parameter, Cristoffel symbol and Covariant differentiation were introduced by mathematicians like Beltrami (1868), Christoffel (1869) and Lipschitz (1869).Schouten and Dantzing (1930, 1931) transferred the results of differential geometry of Riemannian spaces with affine connections to the case of space with complex structure. This opened an era of Complex Manifolds. Ehresmann (1947) defined an almost complex structure manifold carring a tensor field f of type (1, 1) whose square is - In. Weyl (1947) pointed that in a complex manifold, there exists a tensor of type (1, 1) whose square is - In, i.e. f2 = - In. f is called an almost complex structure to Mn.

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Dr Sushil Shukla is working as Assistant Professor (Mathematics), Veer Bahadur Singh Purvanchal University, Jaunpur. His PhD has been awarded (28th August 2007) under the supervision of Prof. P. N. Pandey, Department of Mathematics, University of Allahabad.