The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is fundamental invariant the topology via Mostow-Prasad Rigidity. Motivated by this, second author and Reid defined two-dimensional analogue given multiset isometry types totally geodesic, immersed, finite-area surfaces called geometric genus spectrum. They showed that if $M$ arithmetic contains surface, then det...

M.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined studied the notion of conformal manifolds. In this paper, as a generalization totally real submanifolds maps, we extend almost contact metric manner, introduce from manifolds cosymplectic order guarantee existence notion, give non-trivial example, i...

In this paper, we prove a Second Main Theorem for holomorphic mappings in disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic with respect to meromorphic connection) the complex projective space ℙk. This is generalization Cartan’s Theorem. As consequence, establish uniqueness theorem which intersect O(k3) many totally hypersurfaces.

In this paper we study existence and lack thereof of closed embedded orientable co-dimension one totally geodesic submanifolds minimal volume cusped hyperbolic manifolds.

We study the problem of non-existence totally geodesic complex ball quotients in open Torelli locus a moduli space principally polarized Abelian varieties using analytic techniques.

In this paper, we characterize of totally geodesic Kähler immersions by extrinsic shapes of some curves having points of order 2.

In this paper, we prove that the homology groups of immersed totally geodesic hypersurfaces of compact arithmetic hyperbolic manifolds virtually inject in the homology group of the

In this paper, we establish the following result: Let M be an n-dimensional complete totally real minimal submanifold immersed in CPn with Ricci curvature bounded from below. Then either M is totally geodesic or infr ≤ (3n+1)(n−2)/3, where r is the scalar curvature of M .