Clairaut invariant Riemannian maps with Kahler structure

Clairaut Anti-invariant Riemannian Maps from Kähler Manifolds

“…Theorem 2.1. [9] Let F : (M, g M ) → (N, g N ) be a Riemannian map between Riemannian manifolds such that (rangeF * ) ⊥ is totally geodesic and rangeF * is connected, and let α, β = F • α be geodesic curves on M and N , respectively. Then F is Clairaut Riemannian map with s = e f if and only if any one of the following conditions holds:…”

“…Further, Clairaut submersions were studied in [3], [7] and [8]. In [19] and [9], Clairaut Riemannian maps were introduced by using geodesic curve on the total and base spaces respectively, and obtained necessary and sufficient conditions for Riemannian maps to be Clairaut Riemannian maps. Further, S ¸ahin gave an open problem to find characterizations for Clairaut Riemannian maps (see: [16], p. 165, Open Problem 2).…”

“…Moreover, invariant, anti-invariant and semi-invariant Riemannian maps were studied from a Riemannian manifold to a Kähler manifold [1,2,13,14]. Recently, in [21] and [9], Authors introduced Clairaut invariant and Clairaut anti-invariant Riemannian maps from Riemannian manifolds to Kähler manifolds.…”

“…Further, conformal anti-invariant, semi-invariant Riemannian map from Riemannian manifold to Kähler manifold were introduced in [1,2]. The Clairaut Riemannian maps were introduced in [24], [13] and [12]. Recently, Meena et.…”

“…Recently, Meena et. al have introduced Clairaut invariant [29], anti-invariant [30], and semi-invariant [17] Riemannian maps between Riemannian manifolds and Kähler manifolds. In this article, we discuss about Clairaut slant Riemannian maps.…”