相关论文: Lie groups as four-dimensional special complex man…

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…

We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of various models, both continuous and discrete. This algebraic structure characterizes the isotropic oscillator (with positive, purely imaginary,…

We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two. These foliations produce local complex-valued harmonic…

We find a one-parameter family of non-isomorphic nilpotent Lie algebras $\mathfrak{g}_a$, with $a \in [0,\infty)$, of real dimension eight with (strongly non-nilpotent) complex structures. By restricting $a$ to take rational values, we…

In this paper we use the $Z-$decomposition as a tool to find locally symmetric left invariant Riemannian metrics on some Lie groups. For this purpose, we need to compute the spectrum of the curvature operator. Since the study of this…

We investigate the algebraic structure of complex Lie groups equipped with left-invariant metrics which are expanding semi-algebraic solitons to the Hermitian curvature flow (HCF). We show that the Lie algebras of such Lie groups decompose…

We give a complete classification, up to isometric isomorphism and scaling, of $4$-dimensional metric Lie algebras $(\mathfrak{g},\langle \cdot,\cdot \rangle)$ that admit a non-zero parallel skew-symmetric endomorphism. In particular, we…

We classify, up to homeomorphisms, the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.

On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on…

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they…

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds…

We determine the solvable complete Lie algebras whose nilradical is isomorphic to a filiform Lie algebra. Moreover we show that for any positive integer $n$ there exists a solvable complete Lie algebras whose second cohomology group with…

We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a…

We classify and investigate locally conformally K\"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We describe the full group of isometries of absolutely simple, compact, connected real Lie groups, of SO(4) and of U(n), endowed with suitable bi-invariant Riemannian metrics.

In the present paper we study Randers metics of Berwald type on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. On these spaces, the Randers metrics arising from invariant hyper-Hermitian metrics…

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural…

The $B$-connection on almost complex manifolds with Norden metric is an analogue of the first canonical connection of Lihnerovich in Hermitian geometry. In the present paper it is considered a $B$-connection in the class of the…