In this paper we will introduce a newly found knowledge above the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds and on surfaces on Euclidean space. We will obtain the fundamental equations of rotary diffeomorphisms from (pseudo-) Riemannian manifolds for twice-differentiable metric tensors onto manifolds with affine connections.
In this paper we study conformal holomorphically projective mappings between conformal e-Kähler manifolds K n =.M; g; F / and x K n =. x M ; x g; x F /, i. e. diffeomorphisms f : M 3 x M satisfying f h f 1 f 2 f 3 , where f 1 ; f 3 are conformal mappings and f 2 is a holomorphically projective mapping between e-Kähler manifolds (i. e. Kähler, pseudo-Kähler and hyperbolic Kähler manifolds). Suppose that the initial condition f £ x g h k ¡ g is satisfied at a point x 0 P M and that at this point the Weyl conformal tensor satisfies a certain inequality. We prove that the mapping f is then necessarily conformal.
In this paper, we study holomorphically projective and conformal holomorphically projective mappings between almost Hermitian manifolds Hn = (M, g, F) and [Formula: see text], i.e. diffeomorphism [Formula: see text] satisfying f = f1 ◦ f2 ◦ f3, where f1, f3 are conformal mappings and f2 is a holomorphically projective mapping between almost Hermitian manifolds. We obtain fundamental equations of Cauchy type for holomorphically projective mappings between almost Hermitian manifolds and for above-mentioned mappings a new result for the initial condition [Formula: see text].
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