We determine all the possible pointwise k-symmetric spaces of negative constant curvature. In general, such spaces are not k-symmetric. In fact we show that, for all n>= 3, k not 2, H^n is not k-symmetric, i.e., for any set of selected k-symmetries, one for each point of H^n, the regularity condition does not hold.
Costa, S., Pianta, S., On k-symmetries of hyperbolic spaces, <<DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS>>, 2013; (31): 639-642. [doi:10.1016/j.difgeo.2013.06.003] [http://hdl.handle.net/10807/53662]
On k-symmetries of hyperbolic spaces
Costa, Simone;Pianta, Silvia
2013
Abstract
We determine all the possible pointwise k-symmetric spaces of negative constant curvature. In general, such spaces are not k-symmetric. In fact we show that, for all n>= 3, k not 2, H^n is not k-symmetric, i.e., for any set of selected k-symmetries, one for each point of H^n, the regularity condition does not hold.
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