A survey on paracomplex geometry

DOI10.1216/rmjm/1181072105zbMath0856.53049OpenAlexW1983250767MaRDI QIDQ1915746

V. Cruceanu, Pedro Martínez Gadea, Pedro Fortuny Ayuso

Publication date: 24 February 1997

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL26-1/contents/contents.htm

zbMATH Keywords

paracomplex geometry

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55)

Related Items

Nearly para-Kähler geometry on Lie groups, ON PARASASAKIAN STRUCTURES ON FIVEDIMENSIONAL LIE ALGEBRAS, Some Notes on Berger Type Deformed Sasaki Metric in the Cotangent Bundle, Para-Complex Norden Structures in Cotangent Bundle Equipped with Vertical Rescaled Cheeger–Gromoll Metric, Para‐Hermitian Geometry, Dualities and Generalized Flux Backgrounds, On the Gauss map of equivariant immersions in hyperbolic space, Einstein hypersurfaces in irreducible symmetric spaces, Degenerate multilinear forms and Hermitian and para-Hermitian structures, Octonions as Clifford-like algebras, Clifford structures, bilegendrian surfaces, and extrinsic curvature, SOME RESULTS OF HARMONICITY ON TANGENT BUNDLES WITH φ-SASAKIAN METRICS OVER PARA-KAHLER-NORDEN MANIFOLD, A geometric Laplace method, Geometry of four-dimensional Kähler and para-Kähler Lie groups, F‐Manifolds and geometry of information, Notes About a New Metric on the Cotangent Bundle, Spaces of geodesics of pseudo-Riemannian space forms and normal congruences of hypersurfaces, Almost paracontact almost paracomplex Riemannian manifolds as extensions of 2-dimensional space-forms, Lagrangian foliations and Anosov symplectomorphisms on Kähler manifolds, On 3 -dimensional e J -tangent centro-affine hypersurfaces and e J -tangent affine hyperspheres with some null-directions, Unnamed Item, Paraquaternionic Kähler manifolds, Unnamed Item, Parallel almost paracontact structures on affine hypersurfaces, Nijenhuis operators on pre-Lie algebras, Unnamed Item, NON-EXISTENCE OF PARA-KAHLER–NORDEN WARPED METRICS, A STUDY OF HARMONIC SECTIONS OF TANGENT BUNDLES WITH VERTICALLY RESCALED BERGER-TYPE DEFORMED SASAKI METRIC, Weak para-CR structures on vertical bundles, Special geometry, Hessian structures and applications, Dirac structures and paracomplex manifolds, Chern's conjecture for special affine manifolds, Musical isomorphisms and problems of lifts, Conformally flat Kaluza-Klein spaces, pseudo-/para-complex space forms and generalized gravitational kinks, A note on a paraholomorphic Cheeger-Gromoll metric, Split Special Lagrangian Geometry, Metastring theory and modular space-time, Special geometry of Euclidean supersymmetry. IV: The local c-map, On four-dimensional paracomplex structures with Norden metrics, CURVATURE PROPERTIES OF PSEUDO-SPHERE BUNDLES OVER PARAQUATERNIONIC MANIFOLDS, Extending invariant complex structures, The Ricci tensor of almost Parahermitian manifolds, Holomorphically projective mappings between generalized hyperbolic Kähler spaces, On weakly para-cosymplectic manifolds of dimension 3, Almost Kähler Walker 4-manifolds, Paraholomorphic B-manifold and its properties, On para-complex affine hyperspheres, Deformed Hamiltonian vector fields and Lagrangian fibrations, Second variation for L-minimal Legendrian submanifolds in pseudo-Sasakian manifolds, Non-degenerate para-complex structures in 6D with large symmetry groups, On the integrability of generalized almost para-Norden and para-Hermitian structures, Transplanting geometrical structures, On $\eta $-Einstein para-$S$-manifolds, On $\widetilde{J}$-tangent affine hyperspheres, Bi-Lagrangian structures on nilmanifolds, On Almost Paracontact Almost Paracomplex Riemannian Manifolds, From almost (para)-complex structures to affine structures on Lie groups, Hopf hypersurfaces in complex hyperbolic space and submanifolds in indefinite complex 2-plane Grassmannian. I, On 4-dimensional, conformally flat, almost $\varepsilon$-Kählerian manifolds, On almost hyper-para-Kähler manifolds, Conformal flatness, non-abelian Kaluza-Klein reduction and quaternions, On deformations of D-manifolds and CR D-manifolds, Invariant tensors under the twin interchange of the pairs of the associated metrics on almost paracomplex pseudo-Riemannian manifolds, On holomorphic hypercomplex connections, The bundle of paracomplex structures, Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators, (Para-)Hermitian and (para-)Kähler submanifolds of a para-quaternionic Kähler manifold, The dancing metric, ${G}_2$-symmetry and projective rolling, Conical Ricci-flat nearly para-Kähler manifolds, Generalised kinematics for double field theory, Legendre curves on generalized paracontact metric manifolds, Symplectic, complex and Kähler structures on four-dimensional generalized symmetric spaces, Some notes concerning Riemannian metrics of Cheeger Gromoll type, On small deformations of paracomplex manifolds, Spinors in the hyperbolic algebra, Gravitoelectromagnetism in a complex Clifford algebra, Immersions of Lorentzian surfaces in $\mathbb R^{2,1}$, The noncommutative KdV equation and its para-Kähler structure, Para-CR structures of codimension 2 on tangent bundles in Riemann-Finsler geometry, Pseudo-Riemannian geometry in terms of multi-linear brackets, Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows, A complete classification of four-dimensional para-Kähler Lie algebras, Non-degenerate homogeneous $\epsilon$-Kähler and $\epsilon$-quaternion Kähler structures of linear type, On some differential operators on natural Riemann extensions, Generalized geometric structures on complex and symplectic manifolds, Four-dimensional manifolds with degenerate self-dual Weyl curvature operator, Harmonic vector fields on pseudo-Riemannian manifolds, A spinor approach to Walker geometry, Algebroid structures on para-Hermitian manifolds, Pre-symplectic algebroids and their applications, Para-mixed linear spaces, Harmonic bundle solutions of topological-antitopological fusion in para-complex geometry, The well adapted connection of a $(J^{2}=\pm 1)$-metric manifold, COMPLEX AND PARACOMPLEX STRUCTURES ON HOMOGENEOUS PSEUDO-RIEMANNIAN FOUR-MANIFOLDS, Foliations of semi-Riemannian manifolds, Mean curvature flow of space-like Lagrangian submanifolds in almost para-Kähler manifolds, Complex product structures and affine foliations, Paracomplex paracontact pseudo-Riemannian submersions, A unique connection for Born geometry, Timelike minimal surfaces via loop groups, The geometry of a bi-Lagrangian manifold, On paraquaternionic submersions between paraquaternionic Kähler manifolds, On Bochner flat para-Kählerian manifolds, Cohomology of $\mathbf D$-complex manifolds, Foliation-coupling Dirac structures, Maximally homogeneous para-CR manifolds, Para-Sasaki-like Riemannian manifolds and new Einstein metrics, Generalized Kähler spaces in Eisenhart's sense admitting a holomorphically projective mapping, Unnamed Item, Interpolation of geometric structures compatible with a pseudo Riemannian metric, Paracomplex Hermitean Clifford analysis, Para-Kähler Einstein metrics on homogeneous manifolds, On the vortex filament in 3-spaces and its generalizations, Almost $\alpha$-paracosymplectic manifolds, Almost product structures on statistical manifolds and para-Kähler-like statistical submersions, NOTES ON PARA-NORDEN–WALKER 4-MANIFOLDS, Orientability of linear Weingarten surfaces, spacelike CMC-1 surfaces and maximal surfaces, Para-Kähler-Einstein $4$-manifolds and non-integrable twistor distributions, Neutral slant submanifolds of a para-Kähler manifold, A new type of generalized para-Kähler spaces and holomorphically projective transformations, Geometric realizations of curvature models by manifolds with constant scalar curvature, Riemannian almost product manifolds and submersions. I. II, Para-Hermitian and paraquaternionic manifolds, Berger Type Deformed Sasaki Metric and Harmonicity on the Cotangent Bundle, Wick quantisation of a symplectic manifold, Solutions of Yang-Mills equations on generalized Hopf bundles, Local invariants of divergence-free webs, Structures which are harmonic with respect to Walker metrics

Cites Work