Related papers: On conformally flat totally real submanifolds

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant…

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is…

We show that a real K\"ahler submanifold in codimension $6$ is essentially a holomorphic submanifold of another real K\"ahler submanifold in lower codimension if the second fundamental form is not sufficiently degenerated. We also give a…

This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…

In this short note, we prove the existence of constant scalar curvature K\"ahler metrics on compact K\"ahler manifolds with semi-ample canonical bundles.

We study the basic geometric properties of an indefinite locally conformal Kaehler manifold.

We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…

Four dimensional simply connected Lie groups admitting a pseudo K\"ahler metric are determined. The corresponding Lie algebras are modelized and the compatible pairs $(J,\omega)$ are parametrized up to complex isomorphism (where $J$ is a…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…

Two results regarding K\"ahler supermanifolds with potential $K=A+C\theta\bar\theta$ are shown. First, if the supermanifold is K\"ahler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with K\"ahler potential…

In this paper, we investigate the condition on warped product manifold of a Kenmotsu manifold and the real line to be a conformal Kahler manifold. This result demonstrates the close relation of Kenmotsu and Kahler manifolds.

Let M be a compact complex surface which admits a Kaehler metric whose scalar curvature has integral zero; and suppose the fundamental group of M does not contain an Abelian subgroup of finite index. Then if M is blown up at sufficiently…

We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-K\"{a}hler manifold with negative scalar curvature. We show that this particular complex is exact, with the possible exception of one term.

We classify compact conformally flat $n$-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either $\mathbb{S}^{n}$ with the round metric,…

For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be…

By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…

In this paper, we study the geometry of pointwise semi-slant warped products in a locally conformal Kaehler manifold. In particular, we obtain several results which extend Chen's inequality for CR-warped product submanifolds in Kaehler…

We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds, which we briefly call CPC submanifolds, are always austere, hence minimal, and have constant principal…