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Cross ratios on boundaries of higher rank symmetric spaces. (arXiv:1701.09096v2 [math.DG] UPDATED)
来源于:arXiv
We construct (generalized) cross ratios on Furstenberg boundaries (or flag
manifolds) of higher rank symmetric spaces of non-compact type. We show several
basic properties of it; including continuity, the connection to translation
lengths of hyperbolic elements, and the behavior under products. Moreover, we
motivate that these are suitable generalizations of cross ratios on ideal
boundaries of rank one symmetric spaces, by proving that every continuous cross
ratio-preserving map on the maximal Furstenberg boundary (or full flag
manifold) is induced by an isometry, after multiplying metrics on de Rham
factors by positive constants. If the symmetric space is irreducible this
yields a one-to-one correspondence of isometries and continuous cross
ratio-preserving maps. 查看全文>>