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This book aims to study on a Riemannian manifold admitting a new special type semisymmetric metric connection. Firstly, it contains a brief knowledge on semisymmetric metric connection. It represents a special type of semisymmetric metric connection on a Riemannian manifold. In the last section of this book, it is considered conformally flat manifolds with this new type semisymmetric metric connection. On this manifold, some theorems are proved. Sections 3 and 4, are published as a paper in European Journal of Pure and Applied Mathematics, 4(2), 152161, (2011). In this book, we have studied the subjects in such a way that most of them are simple enough for the readers, at the some time often conveying an interesting geometrical fact.
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