Timeline for Complex manifolds in which the exponential map is holomorphic

7 events

when toggle format	what		by	license	comment
Jun 28, 2011 at 10:35	history	edited	Anton Petrunin	CC BY-SA 3.0	added 204 characters in body
Jun 28, 2011 at 10:30	comment	added	Anton Petrunin		@RdN, Thank you, I will include it in the answer
Jun 28, 2011 at 10:18	history	edited	Anton Petrunin	CC BY-SA 3.0	added 110 characters in body
Jun 25, 2011 at 16:43	comment	added	RdN		I don't quite understand your arguement for exp of a complex line to be totally geodesic. But if so there is a lemma in vol II of Kobayashi Nomizu (Prop. 7.1) that says if two tensors with the symmetry and J invariance of a Kahler curvature tensor agree on complex lines they must be equal. It's clear curves have to be flat by Gauss lemma and totally geodesic would mean the second fundamental vanishes, so we can measure R of the ambient space from such curves. Thus the Prop. says total curvature must vanish.
Jun 24, 2011 at 16:49	history	edited	Anton Petrunin	CC BY-SA 3.0	added 60 characters in body
Jun 24, 2011 at 10:16	history	edited	Anton Petrunin	CC BY-SA 3.0	edited body
Jun 24, 2011 at 10:11	history	answered	Anton Petrunin	CC BY-SA 3.0