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- W276046260 abstract "We provide the basic theory on the conformal geometry of timelike surfaces in pseudo-Riemannian space forms, which is to generalize the fundamental work of Burstall et al. for spacelike surfaces. Then we have a discussion on the transforms of timelike $${(pm)}$$ -isothermic surfaces (or real isothermic, complex isothermic surfaces), including $${c}$$ -polar transforms, Darboux transforms and spectral transforms. The first main result is that c-polar transforms preserve timelike $${(pm)}$$ -isothermic surfaces, which are generalizations of the classical Christoffel transforms. The next main result is that a Darboux pair of timelike isothermic surfaces can also be characterized as a Lorentzian $${O(n-r+1,r+1)/O(n-r,r)times O(1,1)}$$ -type curved flat. Finally two permutability theorems of c-polar transforms are established." @default.
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- W276046260 date "2016-09-27" @default.
- W276046260 modified "2023-10-10" @default.
- W276046260 title "On transforms of timelike isothermic surfaces in pseudo-Riemannian space forms" @default.
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- W276046260 doi "https://doi.org/10.1007/s00025-016-0607-y" @default.
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