Timeline for Do there exist non-totally geodesic isometric minimal immersions $\mathbb{H}^2\rightarrow G/K.$
Current License: CC BY-SA 3.0
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| Apr 8, 2014 at 8:51 | comment | added | Robert Bryant | @AndySanders: You're welcome. If you do want to edit the question, you should only add to it (and note the addition), not remove what's there. (Otherwise, you might make my answer become irrelevant.) I haven't thought about the split case, but I'll do so when I get a chance. If one does have rigidity there, then a proof will likely depend on techniques such as the ones I used in that TAMS article. | |
| Apr 7, 2014 at 22:36 | comment | added | Andy Sanders | Dear Robert, thank you for this excellent answer. Reading it, I realize I should have seen this example coming. I'm not sure if I should revise the question itself, but I'll ask the following refinement here first. What if we assume G is the split real form of a complex, simple Lie group. Perhaps to make things very concrete, SL(n,R)/SO(n) is my first example of interest. I'm new to mathoverflow, so if this refinement should be edited into the original question, I will do so. Thanks! | |
| Apr 7, 2014 at 21:18 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Added an example to address the special case of interest to the OP
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| Apr 7, 2014 at 12:16 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Added an omitted example of a minimal, hyperbolic plane.
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| Apr 7, 2014 at 11:59 | history | answered | Robert Bryant | CC BY-SA 3.0 |