Imperial College London

DrMarie-AmelieLawn

Faculty of Natural SciencesDepartment of Mathematics

Senior Teaching Fellow
 
 
 
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Contact

 

m.lawn

 
 
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Location

 

6M20Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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15 results found

Basilio A, Bayard P, Lawn M-A, Roth Jet al., 2023, Spinorial Representation of Submanifolds in a Product of Space Forms, Advances in Applied Clifford Algebras, Vol: 33, ISSN: 0188-7009

<jats:title>Abstract</jats:title><jats:p>We present a method giving a spinorial characterization of an immersion into a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory for such target spaces. We also study special cases: we recover previously known results concerning immersions in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {S}^2\times \mathbb {R}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and we obtain new spinorial characterizations of immersions in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {S}^2\times \mathbb {R}^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup>

Journal article

Agricola I, Hofmann J, Lawn M-A, 2023, Invariant Spinors on Homogeneous Spheres, Differential Geometry and Its Applications, Vol: 89, ISSN: 0926-2245

Journal article

Daura Serrano J, Kohn M, Lawn M-A, 2022, G-invariant spin structures on spheres, Annals of Global Analysis and Geometry, Vol: 62, Pages: 437-455, ISSN: 0232-704X

<jats:title>Abstract</jats:title><jats:p>We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this classification in two different ways; through examining the differential of the actions and through representation theory.</jats:p>

Journal article

Lawn M-A, Ortega M, 2022, Translating Solitons in a Lorentzian Setting, Submersions and Cohomogeneity One Actions, Mediterranean Journal of Mathematics, Vol: 19, ISSN: 1660-5446

<jats:title>Abstract</jats:title><jats:p>We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify time-like, invariant translating solitons by rotations and boosts in Minkowski space.</jats:p>

Journal article

Lawn M-A, Ortega M, 2019, Associated Families of Surfaces in Warped Products and Homogeneous Spaces, Bulletin of the Belgian Mathematical Society - Simon Stevin, Vol: 26, ISSN: 1370-1444

Journal article

Lawn M-A, Bayard P, Roth J, 2017, SPINORIAL REPRESENTATION OF SUBMANIFOLDS IN RIEMANNIAN SPACE FORMS, Pacific Journal of Mathematics, ISSN: 0030-8730

Journal article

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.

Journal article

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

Journal article

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

Journal article

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

Journal article

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

Journal article

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

Journal article

Lawn M-A, 2008, Immersions of Lorentzian surfaces in R2,1, Journal of Geometry and Physics, Vol: 58, Pages: 683-700, ISSN: 0393-0440

Journal article

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>

Journal article

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

Journal article

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