Clairaut conformal anti-invariant submersions from Kähler manifolds onto Riemannian manifolds
Year: 2026
Type: article
Abstract: This paper studies Clairaut conformal anti-invariant submersions from Kähler manifolds onto Riemannian manifolds. Here, a conformal anti-invariant submersion is a horizontally conformal submersion Φ from a Kähler manifold ( M 1 , g M 1 , J ) onto a Riemannian manifold whose vertical distribution is anti-invariant under the almost complex structure J . A Clairaut conformal anti-invariant submersion is characterized by the existence of a positive girth r such that ( r ∘ α ) sin θ remains constant along every geodesic α of the total manifold, where θ denotes the angle between the tangent vector field of α and the horizontal distribution. Writing r = e f , where f is the logarithmic girth function, characterization results for such geodesics are obtained, and a fundamental Clairaut condition is derived in terms of the O’Neill tensor and ∇ f . Several consequences concerning the position of ∇ f with respect to J ( ker Φ ∗ ) are also established, including a dimension-type alternative for the fibres and conditions under which the logarithmic girth function becomes constant. Furthermore, the harmonicity of Clairaut conformal anti-invariant submersions is investigated, and necessary and sufficient conditions relating the gradient of the logarithmic girth function and the dilation are obtained. Finally, explicit examples illustrating the theory are presented, including a family with non-constant dilation and an example with non-constant logarithmic girth function.
Source: Kuwait Journal of Science
Authors: Murat Polat, Ehsan Foroughi Pournavid
Institution: Dicle University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,100
OpenAlex ID: W7213412643