Unformatted text preview: Diﬀerential Geometry 2
Homework 06 1. Let M be a connected complex manifold (of complex dimension greater
than one) on which g is a K¨hler metric. Show that the only K¨hler metrics
a
a
on M that are conformal to g are the constant multiples of g .
2. Let V, ·· be a complex inner product space. Show explicitly that the
induced fundamental twoform ω on complex projective space P(V ) is closed
so that P(V ) is a K¨hler manifold.
a 1 ...
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This note was uploaded on 07/08/2011 for the course MTG 6256 taught by Professor Robinson during the Spring '09 term at University of Florida.
 Spring '09
 Robinson

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