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Monica Alice Aprodu

Publications and source records attributed to Monica Alice Aprodu.

3 recordsLinked to original sources
arXiv2024

$V$-minimal submanifolds

We introduce the notion of $V$-minimality, for $V$ a smooth vector field on a Riemannian manifold, a natural extension of the classical notion of minimality, and we prove several basic properties. One featured example is given for locally conformal Kaehler (l.c.K) manifolds. It is well-known that in general, complex submanifolds in non-Kaehler l.c.K manifolds are not minimal. We prove that, however, they are $V$-minimal for $V$ a suitable multiple of the Lee vector field. Extending some results from \cite{AAB}, to emphasis the utility of this notion, we prove that a PHH submersion is $V$-harmonic if and only if it has minimal fibres and a PHH $V$-harmonic submersion pulls back complex submanifolds to $V$ minimal submanifolds.

math.DG↗
arXiv2014

Holomorphic vector bundles on Kähler manifolds and totally geodesic foliations on Euclidean open domains

In this Note we establish a relation between sections in globally generated holomorphic vector bundles on Kähler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open domains. We find a geometric condition for a totally geodesic foliation to originate in a holomorphic vector bundle. For codimension-two foliations, this description recovers of P. Baird and J. C. Wood. The universal objects that play a key role are the orthogonal Grassmannians.

math.DG↗