On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

Trend · papers per month

count % of corpus

11 results for “Ricci-parallel”

On pseudo-Riemannian Ricci-parallel Lie groups which are not Einsteinmath.DG

Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.

problem Characterizing and finding non-Einstein pseudo-Riemannian metrics on Lie groups.

method Analyzing left invariant metrics, using double extension process, and constructing examples.

result Construction of infinitely many new explicit examples of non-Einstein pseudo-Riemannian metrics on Lie groups.

Lie groups pseudo-Riemannian metrics Ricci-parallel non-Einstein double extension

2024-04-21abs ↗pdf ↗

Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension

\leq6

math.DG

New metrics with special curvature properties are shown to be parallel in certain Lie groups.

problem Characterizing metrics with harmonic curvature in Lie groups.

method Analyzing left invariant metrics on solvable and low-dimensional Lie groups.

result Left invariant metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension ≤6.

Riemannian metrics harmonic curvature Ricci-parallel solvable Lie groups low-dimensional Lie groups

2021-08-14abs ↗pdf ↗

Identifying Constant Curvature Manifolds, Einstein Manifolds, and Ricci Parallel Manifoldsmath.DG

We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. As applications, constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds are identified, respectively, with different integral-differential formulas and semigroup inequaliti…

2017-10-01abs ↗pdf ↗

Inversion d'opérateurs de courbure au voisinage d'une métrique Ricci parallèlemath.DG

Let $(M,g)$ be a compact riemannian manifold without boundary., with parallel Rici curvature. We show that some operators, affine relatively to the Ricci curvature,are locally invertible, near the metric $g$

2014-04-07abs ↗pdf ↗

Some invariant connections on symplectic reductive homogeneous spacesmath.DG

The paper explores symplectic connections on homogeneous spaces, finding a unique invariant connection.

problem Existence and uniqueness of symplectic connections on symplectic reductive homogeneous spaces.

method Introduced a family of invariant connections and showed the existence of a unique symplectic connection.

result Found a unique symplectic connection

abla^\mathbf{s}

corresponding to

a=b= frac{1}{3}

, which is Ricci-parallel.

symplectic connections homogeneous spaces invariant connections curvature Ricci-parallel

2025-06-29abs ↗pdf ↗

Isoparametric foliation and a problem of Besse on generalizations of Einstein conditionmath.DG

The focal sets of isoparametric hypersurfaces in spheres with g = 4 are all Willmore submanifolds, being minimal but mostly non-Einstein ([TY1], [QTY]). Inspired by A.Gray's view, the present paper shows that, these focal sets are all A- manifolds but rarely Ricci parallel, except possibly for the only unclassified cas…

2013-07-15abs ↗pdf ↗

On focal submanifolds of isoparametric hypersurfaces and Simons formulamath.DG

The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $\mathcal{A}$ -manifolds in the sense of A.Gray but rarely Ricci-parallel (\cite{QTY},\cite{LY},\cite{TY3}). In this paper we study the geometry of the focal submanifolds via Simons formula. We show that …

2015-01-28abs ↗pdf ↗

Maximally-warped metrics with harmonic curvaturemath.DG

We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only simple eigenvalues. We also prove that, in every given dimension greater than tw…

2018-12-14abs ↗pdf ↗

Rigidity results for Riemannian twistor spaces under vanishing curvature conditionsmath.DG

The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.

problem Characterizing Riemannian twistor spaces under vanishing curvature conditions.

method Moving frame method, classification, and nonexistence proofs.

result The only twistor space with parallel Bochner tensor is

\mathbb{CP}^3

twistor spaces Riemannian manifolds curvature conditions moving frame classification

2022-06-29abs ↗pdf ↗

A note on Einstein metrics and Riemannian twistor spacesmath.DG

Study classifies certain Einstein 4-manifolds with twistorial properties.

problem Classifying Einstein manifolds with positive scalar curvature.

method Proving properties of Einstein four-manifolds and their twistor spaces.

result Compact Einstein four-manifolds with positive scalar curvature and specific twistorial conditions are

\mathbb{S}^4

and

\mathbb{CP}^2

Einstein manifolds twistor spaces Riemannian geometry scalar curvature positive curvature

2025-07-21abs ↗pdf ↗

On the Ricci symmetries of a Kähler manifoldmath.DG

The paper explores symmetries in Kähler manifolds using Ricci tensor properties.

problem Investigating symmetries in Kähler manifolds involving Ricci tensor.

method Analyzing properties of Kähler-Einstein spaces and their generalizations.

result Clarified the geometric role of holomorphic Ricci pseudosymmetry and established new criteria for Kähler manifolds to be Einstein.

Kähler manifold Ricci tensor symmetry holomorphic plane Einstein manifold

2026-05-14abs ↗pdf ↗