Contactly geodesic transformations of almost-contact metric structures
For two pseudo-Riemannian manifolds \((M,g)\) and \((\overline M,\overline g)\) a diffeomorphism \(\varphi: M\to\overline M\) is called a geodesic map if \(\varphi\) takes any geodesic in \(M\) to a geodesic in \(\overline M\). \(M\) inherits a new pseudo-Riemannian metric \(\varphi^*\overline g\) which is referred to as a geodesic transformation of the initial metric. Let \(A{\mathcal C}\) be an almost contact structure on a \((2m+1)\)-dimensional pseudo-Riemannian manifold \(M\). A geodesic transformation of the metric of \(A{\mathcal C}\)-structure is said to be contactly geodesic, or briefly \(c\)-geodesic if \(M\) with this transformed metric admits an \(A{\mathcal C}\)-structure. In the case when \(A{\mathcal C}\) is normal in the sense of \textit{V. F. Kirichenko} [Differential-geometric structures on manifolds, Moscow State Pedagogical Univ., Moscow (2003)], it is shown that any \(c\)-geodesic transformation of the metric takes any normal \(A{\mathcal C}\)-structure to a normal \(A{\mathcal C}\)-structure, while a cosymplectic manifold admits no nontrivial \(c\)-geodesic transformation of the metric. The latter statement remains true for Sasakian or Kenmotsu contact manifolds.
scientific article; zbMATH DE number 5155517