We prove the classical Yano-Obata conjecture by showing that the connected component of the group of holomorph-projective transformations of a closed, connected Riemannian Kähler manifold consists of isometries unless the metric has constant positive holomorphic curvature.
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.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Yano's proof”
Integral foliated simplicial volume vanishes for manifolds with -action.
problem Integral foliated simplicial volume of manifolds with -action.
method Geometric construction of Yano's proof for ordinary simplicial volume combined with parametrised uniform boundary condition for .
result Integral foliated simplicial volume of aspherical manifolds with -action vanishes.
Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.
problem Understanding local diffeomorphisms of conformal circles.
method Variations of conformal circles and pseudo-Riemannian manifolds.
result Local diffeomorphisms of conformal circles are conformal local diffeomorphisms.
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…
Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.
problem Understanding the rigidity of Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds.
method Defining -gradations and filtrations, showing trivial second cohomology groups, and proving non-deformability.
result Killing-Yano and conformal Killing-Yano superalgebras are rigid and correspond to geometric invariants of constant curvature manifolds.
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a gr…
Two Kähler metrics on a complex manifold are called c-projectively equivalent if their -planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…
Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.
problem Derive Minkowski formula for conformal Killing-Yano 2-forms.
method Analyze spacetime Alexandrov theorem with a free boundary.
result Established spacetime Alexandrov theorem with a free boundary.
Study finds only complex 2-step nilpotent Lie groups have Killing-Yano forms.
problem Characterizing Lie groups with Killing-Yano forms.
method Analyzing 2-step nilpotent Lie groups and connected graphs.
result Only complex 2-step nilpotent Lie groups have non-degenerate Killing-Yano forms.
New currents derived from Killing-Yano tensors for gravity.
problem Finding new conserved currents in gravity.
method Using relations involving Riemann, Ricci, and Einstein tensors to introduce novel conserved currents.
result New currents derived from Killing-Yano tensors and their implications for conserved charges.
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, th…
The study classifies special flows on specific geometric groups.
problem Classifying special flows on specific geometric groups.
method Classification of Left-invariant Ricci collineations associated to Yano connections on three-dimensional Lorentzian Lie groups.
result Results in classifying these flows.
The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momen…
We show that the Euclidean Kerr-NUT-(A)dS metric in dimensions locally admits hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided its exterior derivativ…
We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.
Harmonic spinors linked to twistor spinors via potential forms and conformal Killing-Yano forms.
problem Connecting harmonic spinors and twistor spinors using mathematical operators.
method Constructing symmetry operators from conformal Killing-Yano forms and finding transformation operators between twistor and harmonic spinors in terms of potential forms.
result Operators transforming gauged twistor spinors to gauged harmonic spinors and algebraic conditions for Seiberg-Witten equations solutions.
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
Extended supersymmetry leads to Yano F structures on a manifold.
problem Exploring the geometry of extended supersymmetry.
method Using a symplectic sigma model, the paper constructs a geometry on the doubled tangent bundle with two Yano F structures.
result The algebra closure and invariance of the action are discussed and shown to hold.
We give a rigorous geometric proof of the Murakami-Yano formula for the volume of a hyperbolic tetrahedron. In doing so, we are led to consider generalized hyperbolic tetrahedra, which are allowed to be non-convex, and have vertices `beyond infinity'; and we uncover a group, which we call 22.5K, of 23040 scissors-class…
Researchers derive symmetry operators from twistor spinors in curved spacetime.
problem Deriving symmetry operators for gauged twistor spinors in curved backgrounds.
method Using gauged twistor spinors and conformal Killing-Yano forms, symmetry operators are constructed.
result Symmetry operators can be obtained from ordinary twistor spinors in constant curvature backgrounds.
The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos li…
Generically, the set of points along which two non-singular vector fields on the three-sphere are positively (resp. negatively) collinear form a link. We prove that the two vector fields are homotopic if and only if the linking number of those links is zero. We use this criterion to give a new proof of a result of Yano…
Estimates quasi-local mass using Minkowski formula and conformal Killing-Yano forms.
problem Estimating quasi-local mass in various spacetimes.
method Applying Minkowski formula to conformal Killing-Yano forms in different spacetimes.
result Obtains rigidity theorems characterizing spacetimes.
Classes d'homotopie de champs de vecteurs Morse-Smale sans singularité sur les fibrés de Seifertmath.DS
In the first part of this paper, we consider smooth maps from a compact orientable 3-manifold without boundary to the 2-sphere. We give a geometric criterion to decide whether two given maps are homotopic, based on the sets of points where the maps are equal or antipodal. We extend this criterion to non-singular vector…
A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that a volume formula for ordinary hyperbolic tetrahedra devised by J. Murakami and M…
Study shows complex affine transformations index is at most 2 for Kähler manifolds.
problem Understanding transformations on Kähler manifolds.
method Analyzing groups of transformations on Kähler manifolds.
result Establishes a stronger version of Yano-Obata conjecture for complete Kähler manifolds.
Study BGG operators on homogeneous conformal geometries.
problem Finding solutions to BGG operators on homogeneous conformal geometries.
method Invariant calculus for algebraic computations.
result Explicit solutions found for conformal Killing tensors, forms, and spinors.
The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.
problem Generalizing twistor spinors to Kähler manifolds.
method Finding differential equations and reducing them to conformal Killing-Yano equations.
result Bilinear forms of Kählerian twistor spinors reduce to Kählerian conformal Killing-Yano equations under certain conditions.
Researchers describe a method to construct Ricci-flat metrics on a specific surface.
problem Constructing Ricci-flat metrics on a del Pezzo surface.
method Developed a framework and explicitly constructed the first-order deformation of the orthotoric metric.
result The deformation of the conformal Killing-Yano form does not exist.
This paper reviews golden Riemannian manifolds over the past decade.
problem Exploring the properties and applications of golden Riemannian manifolds.
method Comprehensive review of existing literature.
result A detailed survey of golden Riemannian manifolds from 2008 to present.
Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetimehep-th
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…
The paper proves Liouville-type theorems on Hadamard manifolds.
problem Non-existence of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on Hadamard manifolds.
method Proofs use Liouville-type theorems on non-existence of subharmonic and harmonic functions on complete Riemannian manifolds, modified for Hadamard manifolds.
result Proves several Liouville-type theorems on Hadamard manifolds.
Survey of weak metric f-manifolds, generalizing K. Yano's structures.
problem Generalizing K. Yano's f-structures to new types of manifolds.
method Exploring new structures and properties of weak metric f-manifolds.
result New applications in geometry, including Killing vector fields and Ricci-type solitons.
New formulation of Schrödinger connections preserves vector lengths in geometry.
problem Preserving vector lengths in non-Euclidean geometries.
method Coordinate-free formulation, differential geometry, torsion, non-metricity.
result Explicit example of non-static Einstein manifold with torsion.
Extends symmetry superalgebras to include all hidden symmetries of manifolds.
problem Tackles hidden symmetries of manifolds generated by Killing spinors.
method Defines generalized symmetry superalgebras, constructs Lie algebra structure, and defines symmetry operators.
result Constructs special Killing-Yano and conformal Killing-Yano forms from bilinears of Killing spinors.
New definitions and properties of harmonic vector fields on Finsler manifolds.
problem Defining and understanding harmonic vector fields in Finsler geometry.
method Natural definitions of differential, divergence, and -harmonic form; proving Hodge theorem; Bochner-Yano classification theorem.
result A closed orientable Finsler manifold with a positive harmonic Ricci scalar has a zero Betti number.
It has been shown that for each Killing-Yano (KY)-form accepted by an -dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general ge…
New structures defined for studying contact foliations and their geometry.
problem Understanding dynamics of contact foliations and their applications.
method Define and study weak nearly S- and weak nearly C-structures.
result Characterize weak nearly S- and weak nearly C- submanifolds in weak nearly Kähler manifolds.
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
problem Classifying and understanding CKY 2-forms on 5D Lie groups.
method Classification and analysis of 5D metric Lie algebras with CKY tensors.
result First examples of CKY 2-forms on metric Lie algebras without Sasakian structures.
Study finds all hyper-Kähler 4-manifolds with specific symmetries and structures.
problem Characterizing hyper-Kähler 4-manifolds with conformal Kähler structures.
method Analyzing twistor elementary states and locally flat spaces, showing compatibility and incompatibility of complex structures.
result Only hyper-Kähler 4-metric with a non-constant Killing-Yano tensor is the half-flat Taub-NUT instanton.
Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.
problem Constructing extended superalgebras from twistor and Killing spinors.
method Using twistor and Killing spinors, symmetry operators, and KY/CKY forms, extended superalgebras are constructed.
result Extended Killing and conformal superalgebras are constructed in constant curvature and Einstein manifolds.
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …
We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized -structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized complex structures on product manifolds in which one factor is a Lie group and we gen…
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases via dilogarithm functions and to treat properly the many analyti…
Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic cl…
We classify all spacetimes with a closed rank-2 conformal Killing-Yano tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness condition…
Bochner-Yano Type Theorems for Conformal Killing Vector Fields under Curvature Pinching Conditionsmath.DG
The study proves that conformal Killing vector fields on manifolds with positive Ricci curvature are non-trivial.
problem Investigating conformal Killing vector fields on manifolds under curvature pinching conditions.
method Establishing a new Bochner-type identity and using Moser iteration for gradient estimates.
result Conformal Killing vector fields are non-trivial on manifolds with positive Ricci curvature.
A generalization to the almost complex setting of a well-known result by S. Webster is given. Namely, we prove that if is a strongly pseudoconvex hypersurface in an almost complex manifold , then the conormal bundle of is a totally real submanifold of $(T^*M, \J)$, where $\J$ is the lifted almost comple…