Can someone suggest a book on complex geodesic flow? I am interested in it mainly because I was told these form a very useful class of Riemann surface laminations. Of special interest to me is the case when the leaves are hyperbolic. Please give your suggestions. Thanks in advance.
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asked Jun 21, 2017 at 17:52
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2$\begingroup$ Can you explain what precisely you mean by the complex geodesic flow? The terminology is unfamiliar to me. Are you looking for references for the dynamics of the geodesic flow on complex space forms? $\endgroup$– ClarkCommented Jun 26, 2017 at 2:36
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$\begingroup$ The fact is that I do not know the definition myself - yes, it is embarrassing. It was mentioned in passing at a place and I wanted to learn more about it. The only thing I understood is that it is the complex analogue of geodesic flows. Instead of flowing along a vector you flow along a plane - whatever that means. Understanding this concept would be of great use to me. Thanks for taking interest. $\endgroup$– Divakaran DivakaranCommented Jun 26, 2017 at 5:33
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$\begingroup$ This notion should generalize the following: given a complex space form $M$ ($\mathbb{C}\mathbb{P}^{n}$, $\mathbb{C}^{n}$, or $\mathbb{C}\mathbb{H}^{n}$)) any geodesic $\gamma$ is isometrically contained inside a totally geodesic Riemann surface $S$. These surfaces are referred to as complex geodesics in the literature (e.g. in Teichmueller theory). Note: deleted and replaced a previous version of this comment which misstated the above. $\endgroup$– ClarkCommented Jun 26, 2017 at 23:14
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