This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli-Chern class on compact complex manifolds, and proved that the curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. …
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48 results for “Levi-Civita”
In this paper, we study the geometry of compact complex manifolds with Levi-Civita Ricci-flat metrics and prove that compact complex surfaces admitting Levi-Civita Ricci-flat metrics are Kahler Calabi-Yau surfaces or Hopf surfaces.
Derives Levi-Civita connection formulas for specific geometries.
problem Determining geometric invariants of Lorentzian manifolds.
method Explicitly derives Christoffel symbols in terms of adapted frame fields.
result Formulas for geometric invariants of Lorentzian manifolds.
Study on null-projectability of Levi-Civita connections in neutral metrics.
problem Characterizing projectability of Levi-Civita connections along null parallel distributions.
method Analyzing projectability of torsion-free connections along foliations on manifolds, focusing on neutral metric signatures and mid-dimensional distributions.
result Extension of Patterson and Walker's Riemann extension metrics to null parallel distributions of any dimension.
Study finds all conformal Ricci collineations on specific 3D Lorentzian groups.
problem Identifying conformal Ricci collineations on three-dimensional Lorentzian Lie groups.
method Analysis of Levi-Civita connection on specific Lie groups.
result Determined all conformal Ricci collineations associated with the Levi-Civita connection.
For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theore…
The paper proves unique Levi-Civita connections on noncommutative forms.
problem Existence and uniqueness of Levi-Civita connections on noncommutative differential forms.
method Combining Hilbert module and algebraic techniques, proving conditions for existence and uniqueness of Hermitian torsion-free connections.
result Existence and uniqueness of Levi-Civita connections on θ-deformations of compact Riemannian manifolds.
Constructs a unique Levi-Civita connection for generalised metrics.
problem Non-uniqueness of generalised Levi-Civita connections.
method Geometrically constructs a canonical generalised Levi-Civita connection.
result Decomposes the generalised Riemann curvature tensor in terms of classical geometric data.
The paper studies curvatures in metric Jordan algebras, proving unique connections and curvature formulas.
problem Investigating curvatures in metric Jordan algebras.
method Defined the Jordan-Levi-Civita connection, introduced curvature tensors, and proved curvature formulas.
result Every formally real Jordan algebra admits a metric of non-positive Jordan curvature and a Jordan-Einstein metric of negative Jordan scalar curvature.
Solves Lie's 3D metric problem for projective vector fields.
problem Describing 3D Levi-Civita metrics with non-trivial projective vector fields.
method Analyzes Riemannian and Levi-Civita metrics of arbitrary signature.
result Solves the analog of Lie's problem in 3D.
Geometric structures in math.DG
The paper studies geometric structures in Sol_3 with two connections.
problem Analyzing geometric structures in Sol_3 using specific connections.
method Used Levi-Civita and semi-symmetric non-metric connections to study Sol_3.
result Concluded geometric structures in Sol_3 with both connections.
As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its Levi-Civita connection? It is shown that for a generic…
Classifies Calabi hypersurfaces with parallel Fubini-Pick form.
problem Classifying Calabi hypersurfaces with specific geometric properties.
method Classification based on parallel Fubini-Pick form and Levi-Civita connection.
result Classification of 2 and 3-dimensional Calabi hypersurfaces.
In this paper, we prove a local index theorem for the DeRham Hodge-laplacian which is defined by the connection compatible with metric. This connection need not be the Levi-Civita connection. When the connection is Levi-Civita connection, this is the classical local Gauss-Bonnet-Chern theorem.
A diffeological connection on a diffeological vector pseudo-bundle is defined just the usual one on a smooth vector bundle; this is possible to do, because there is a standard diffeological counterpart of the cotangent bundle. On the other hand, there is not yet a standard theory of tangent bundles, although there are …
The basic class of the non-integrable almost complex manifolds with a pair of Norden metrics are considered. The interconnections between corresponding quantities at the transformation between the two Levi-Civita connections are given. A 4-parametric family of 4-dimensional quasi-Kaehler manifolds with Norden metric is…
Finite element approximation of the Levi-Civita connection and its curvature in two dimensionsmath.NA
The paper approximates Levi-Civita connection and curvature on 2D manifolds using finite elements.
problem Approximating Levi-Civita connection and curvature on 2D manifolds with finite elements.
method Using Regge finite elements, piecewise polynomial symmetric (0,2)-tensor fields, and distributional sense for non-regular tensors.
result Distributional quantities converge to their smooth counterparts under refinement of triangulation.
We build metrized quantum vector bundles, over a generically transcendental quantum torus, from Riemannian metrics, using Rosenberg's Levi-Civita connections for these metrics. We also prove that two metrized quantum vector bundles, corresponding to positive scalar multiples of a Riemannian metric, have distance zero b…
We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank (non-degenerate) contravariant tensor field. We describe the difference between odd Riemannian and odd symplectic structure in terms of the Cartan prolongation of the corresponding Lie algebras, and formulate an an…
New derivation of Type IIA flow metrics.
problem Flow of metrics in Type IIA theory.
method Adapted to Laplacian flow, uses projected Levi-Civita connection.
result New derivation of flow equations.
Geometric calculations on probability manifolds from reciprocal relations in Master equationsmath-ph
The paper explores geometric calculations on probability manifolds derived from master equations.
problem Understanding geometric properties of probability manifolds from master equations.
method Deriving geometric quantities like Levi-Civita connection, gradient, Hessian, parallel transport, and curvatures on probability manifolds.
result Calculation of geometric quantities in probability manifolds, including curvatures and connections.
Defines and classifies algebraic Schouten solitons in 3D Lorentzian Lie groups.
problem Classifying solitons in 3D Lorentzian Lie groups.
method Defined algebraic Schouten solitons and classified them for specific connections.
result Classified algebraic Schouten solitons for various connections on 3D Lorentzian Lie groups.
The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection and semisymmetric metric connection and obtain that these two classes are equivalent with a certain condition. Also the invariant and anti-inv…
Torsion-free connections on -structures are proven for certain groups.
problem Proving torsion-free connections on -structures for specific groups.
method Classification of admissible groups and construction of connections.
result Torsion-free connections can be locally Levi-Civita connections in a given conformal class.
Study on -structures manifold geometry.
problem Understanding the space of closed -structures.
method Developed Sobolev-type metrics, Levi-Civita connections, geodesic equations.
result Formulated variational structures of torsion-free -structures.
Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi-Civita connectio…
Let Riemannian metrics and on a connected manifold have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the famous Levi-Civita's Theorem, the metrics have a certain standard form near the…
New metrics found on non-Kähler Calabi-Yau manifolds.
problem Finding Levi-Civita Ricci-flat metrics on non-Kähler Calabi-Yau manifolds.
method Constructing new metrics on specific types of non-Kähler Calabi-Yau manifolds.
result Examples of Levi-Civita Ricci-flat metrics on various non-Kähler Calabi-Yau manifolds.
Study flat connections on Courant algebroids using Lie groups.
problem Flatness conditions on Courant algebroids.
method Metric generalized connections, flatness condition analysis.
result Existence of compact simple Lie groups as building blocks for flat transitive Courant algebroids.
Study of convex hypersurfaces with specific curvature properties.
problem Characterizing convex hypersurfaces with vanishing Weyl curvature and semi-parallel cubic form.
method Analyzing locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of affine metric.
result Classification of such hypersurfaces, excluding flat affine metric cases.
This paper classifies hypersurfaces in n+1 with parallel Fubini-Pick form.
problem Classifying hypersurfaces with parallel Fubini-Pick form in \(\mathbb{R}^{n+1}\).
method Defining a generalized Calabi product and proving decomposition theorems.
result Complete classification of Calabi hypersurfaces in \(\mathbb{R}^{n+1}\) with parallel Fubini-Pick form.
Study of manifolds with flat connections and diagonal metrics leading to vanishing Euler characteristic.
problem Understanding the geometry and topology of affine-orthogonal manifolds.
method Deformation of flat connections into Levi-Civita connections and analysis of Euler characteristic.
result Deformations force the Euler characteristic to vanish, supporting Chern's conjecture.
Study odd generalized Einstein metrics on 3D Lie groups.
problem Classify odd generalized Einstein metrics on 3D Lie groups.
method Left-invariant generalized connections, divergence operators, and Ricci tensors.
result Describe all odd generalized Einstein metrics on all 3D Lie groups.
Defines a new natural connection on Riemannian Π-manifolds.
problem Characterizing natural connections on Riemannian Π-manifolds.
method Introducing and analyzing the first natural connection with torsion.
result Relations between the first natural connection and Levi-Civita connection are established.
This paper (the seventh paper in a series of eight) continues the development of our theory of multivector and extensor calculus on smooth manifolds. Here we deal first with the concepts of ordinary Hodge coderivatives, duality identities, and Hodge coderivative identities. Then, we recall the concept of a Levi-Civita …
In this paper, we introduce the first Aeppli-Chern class for complex manifolds and show that the - component of the curvature -form of the Levi-Civita connection on the anti-canonical line bundle represents this class. We systematically investigate the relationship between a variety of Ricci curvatures on Her…
Develops Palatini formalism in generalized geometry for string theory.
problem Formulating Palatini variation in generalized geometry.
method Palatini formalism within generalized Riemannian geometry of Courant algebroids.
result Natural emergence of generalized Levi-Civita connection and string effective actions.
Study on harmonicity of complex structure on product of trans-Sasakian manifolds.
problem Investigating harmonicity of complex structure on product of trans-Sasakian manifolds.
method Analysis of Levi-Civita connection and conditions for harmonicity on product manifold.
result Conditions for harmonicity of complex structure on product manifold of trans-Sasakian manifolds.
Classifies Weyl structures on compact conformal manifolds with special holonomy.
problem Classifying Weyl structures on compact conformal manifolds with specific holonomy properties.
method Analyzes the properties of connections preserving the conformal structure and classifies structures based on their holonomy.
result Local classification of Weyl structures on compact conformal manifolds with special holonomy.
This thesis contains an introduction to the method of average in Finsler geometry. The method is applied to Berwald spaces, obtaining geodesic rigidity conditions. We prove that the Levi-Civita connection of any Riemannian metric affine equivalent to the Berwald metric leaves invariant the indicatrix of th Finsler metr…
Study geodesics on a modified cotangent bundle over Kählerian manifolds.
problem Investigate geodesics on a modified cotangent bundle.
method Introduced Berger-type deformed Sasaki metric, investigated Levi-Civita connections, and studied geodesics.
result Geodesic properties on modified cotangent bundles.
Study of degenerate contrast functions on Lie groupoids and their geometric structures.
problem Understanding geometric structures on Lie groupoids with degenerate metrics.
method Using Lie groupoids and algebroids, analyze contrast functions and degenerate two-forms.
result Reduction of degenerate two-forms to pseudometric structures under regular conditions.
We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this con…
In this article I will prove new representation for the Levi-Civita connection in terms of the stochastic flow corresponding to Brownian motion on manifold.
Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.
problem Exploring geometric and harmonic properties of new metrics.
method Conformal deformation of Berger-type metric, analysis of Levi-Civita link, study of curvature varieties, and harmonic maps.
result Detailed examination of curvature varieties and harmonic maps on the manifold.
The paper classifies translation surfaces with constant curvature in a specific connection.
problem Classifying translation surfaces with constant curvature in a semi-symmetric non-metric connection.
method Completely classified translation surfaces of constant sectional curvature in a semi-symmetric non-metric connection.
result Translation surfaces of constant curvature are generalized cylinders, similar to the Levi-Civita connection but with additional non-constant curvature cases.
The paper studies Riemannian metrics on Lie groups with specific commutator subgroups.
problem Investigating Riemannian metrics on Lie groups with commutator subgroups of dimensions 1 and 2.
method Explicitly provided Levi-Civita connection, sectional curvature, and Ricci curvature; computed necessary and sufficient conditions for Ricci solitons; characterized Ricci solitons on Lie groups with one-dimensional commutator subgroups; examined indecomposable Lie groups with two-dimensional commutator subgroups.
result Characterization of all Ricci solitons on Lie groups with one-dimensional commutator subgroups and examination of indecomposable Lie groups with two-dimensional commutator subgroups.