10 results found
Lawn M-A, Bayard P, Roth J, 2017, SPINORIAL REPRESENTATION OF SUBMANIFOLDS IN RIEMANNIAN SPACE FORMS, Pacific Journal of Mathematics, ISSN: 0030-8730
Lawn M-A, Roth J, 2017, A fundamental theorem for submanifolds of multiproducts of real space forms, Advances in Geometry, Vol: 17, ISSN: 1615-7168
We prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then we prove the existence of associate families of minimal surfaces in such products. Finally, in the case of 2 × 2, we give a complex version of the main theorem in terms of the two canonical complex structures of 2 × 2.
Lawn M-A, Ortega M, 2015, A fundamental theorem for hypersurfaces in semi-Riemannian warped products, Journal of Geometry and Physics, Vol: 90, Pages: 55-70, ISSN: 0393-0440
Bayard P, Lawn M-A, Roth J, 2013, Spinorial representation of surfaces into 4-dimensional space forms, Annals of Global Analysis and Geometry, Vol: 44, Pages: 433-453, ISSN: 0232-704X
ALTOMANI A, LAWN M-A, 2013, Isometric and CR pluriharmonic immersions of three dimensional CR manifolds in Euclidean spaces, Hokkaido Mathematical Journal, Vol: 42, ISSN: 0385-4035
Lawn M-A, Roth J, 2011, Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms, Mathematical Physics, Analysis and Geometry, Vol: 14, Pages: 185-195, ISSN: 1385-0172
Lawn M-A, Roth J, 2010, Isometric immersions of hypersurfaces in 4-dimensional manifolds via spinors, Differential Geometry and its Applications, Vol: 28, Pages: 205-219, ISSN: 0926-2245
Lawn M-A, 2008, Immersions of Lorentzian surfaces in R2,1, Journal of Geometry and Physics, Vol: 58, Pages: 683-700, ISSN: 0393-0440
CORTÉS V, LAWN M-A, SCHÄFER L, 2006, AFFINE HYPERSPHERES ASSOCIATED TO SPECIAL PARA-KÄHLER MANIFOLDS, International Journal of Geometric Methods in Modern Physics, Vol: 03, Pages: 995-1009, ISSN: 0219-8878
<jats:p> We prove that any special para-Kähler manifold is intrinsically an improper affine hypersphere. As a corollary, any para-holomorphic function F of n para-complex variables satisfying a non-degeneracy condition defines an improper affine hypersphere, which is the graph of a real function f of 2n variables. We give an explicit formula for the function f in terms of the para-holomorphic function F. Necessary and sufficient conditions for an affine hypersphere to admit the structure of a special para-Kähler manifold are given. Finally, it is shown that conical special para-Kähler manifolds are foliated by proper affine hyperspheres of constant mean curvature. </jats:p>
Lawn MA, Schäfer L, 2005, Decompositions of para-complex vector bundles and para-complex affine immersions, Results in Mathematics, Vol: 48, Pages: 246-274, ISSN: 0378-6218
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