In this paper, we study the horizontal Newton transformations, which are nonlinear operators related to the natural splitting of the second fundamental form for hypersurfaces in a complex space form. These operators allow to prove the classical Minkowski formulas in the case of real space forms: Unlike the real case, the horizontal ones are not divergence-free. Here, we consider the highest order of nonlinearity and we will show how a Minkowski-type formula can be obtained in this case.
Guidi C., Martino V. (2021). Horizontal Newton operators and high-order Minkowski formula. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 23(2), 1-19 [10.1142/S0219199720500042].
Horizontal Newton operators and high-order Minkowski formula
Guidi C.
;Martino V.
2021
Abstract
In this paper, we study the horizontal Newton transformations, which are nonlinear operators related to the natural splitting of the second fundamental form for hypersurfaces in a complex space form. These operators allow to prove the classical Minkowski formulas in the case of real space forms: Unlike the real case, the horizontal ones are not divergence-free. Here, we consider the highest order of nonlinearity and we will show how a Minkowski-type formula can be obtained in this case.| File | Dimensione | Formato | |
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