arXiv subjects
Publications and source records attributed to Dan Radu Latcu.
We provide necessary and sufficient conditions for a $3$-dimensional submanifold of $\mathbb R^3$ endowed with a diagonal metric to be flat. As applications, we characterize the flat manifolds of warped product-type, more precisely, the warped, biwarped, sequential warped, and doubly warped product manifolds, and we state the corresponding nonexistence results.
We study some properties of pointwise $k$-slant submanifolds of almost Hermitian manifolds with a special view towards Kähler manifolds. In particular, we characterize the integrability of the component distributions, treating also the totally geodesic case.
We consider almost Einstein solitons $(V,λ)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $λ$ by means of the gradient vector field $V$ and illustrate the result with suitable examples. Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.
We study almost Riemann solitons and almost Ricci solitons in an $(α,β)$-contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear with the structure vector field.