Nearly K Hler Manifold (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a nearly K hler manifold is an almost Hermitian manifold M, with almost complex structure J, such that the (2,1)-tensor \nabla J is skew-symmetric. So, for every vectorfield X on M. In particular, a K hler manifold is nearly K hler. The converse is not true. The nearly K hler six-sphere S6 is an example of a nearly K hler manifold that is not K hler. The familiar almost complex structure on the six-sphere is not induced by a complex atlas on S6. A nearly K hler manifold should not be confused with an almost K hler manifold. An almost K hler manifold M is an almost Hermitian manifold with a closed K hler form: d = 0. The K hler form or fundamental 2-form is defined by where g is the metric on M. The nearly K hler six-sphere is an example of a nearly K hler manifold that is not almost K hler.