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# Publications by Prof. Mike Crampin

Recent publications of Mike Crampin (For joint publications, see the list of the research unit).

PS-files can be viewed with Ghostview

M. Crampin, Finsler functions for two-dimensional sprays.

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M. Crampin, On the construction of Riemannian metrics from Berwald spaces by averaging. Houston J Math. 40(3) 2014 pp. 737-750.

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M. Crampin and D.J. Saunders, Homogeneity and projective equivalence of differential equation fields. J Geom Mech 4 (2012) 27-47.

[arXiv]

M. Crampin, Homogeneous systems of higher-order ordinary differential equations, Comm. Math. 18 (2011) 37-50.

[journal]

D.J. Saunders and M. Crampin, The fundamental form of a homogeneous Lagrangian in two independent variables, J. Geom. Phys. 60 (2010) 1681 - 1697.

[arXiv] [doi]

M. Crampin and D.J. Saunders, Holonomy of a class of bundles with fibre
metrics. Publicationes Mathematicae Debrecen 81 (2012) 199-234.

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M. Crampin, Cartan connections and Lie algebroids. SIGMA 5 (2009) 061.

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M. Crampin, On Landsberg spaces and the Landsberg-Berwald problem, Houston J Math 37 (2011) 1103-1124.

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M. Crampin and D.J. Saunders, Homotopy operators for the variational bicomplex, representations of the Euler-Lagrange complex, and the
Helmholtz-Sonin conditions,
Lobachevskii J. Math. 30 (2009) 107-123.

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M. Crampin, Some remarks on the Finslerian version of Hilbert's fourth problem, Houston J Math 37 (2011) 369-391.

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M. Crampin, Structural equations for a special class of conformal Killing tensors of arbitrary valence.
Rep. Math. Phys. 62 (2008) 241-254.

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M. Crampin and D.J. Saunders, Some concepts of regularity for parametric multiple-integral problems in the
calculus of variations. Czech. Math. J. 59 (2009) 741-758.

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M. Crampin,
Concircular vector fields and special conformal Killing tensors
In: Differential Geometric Methods in Mechanics and Field Theory (ed
Cantrijn, Crampin and Langerock) Academia Press, Gent (2007)57-70.

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M. Crampin and D.J. Saunders, On the geometry of higher-order ordinary differential equations and the Wuenschmann invariant. In: Groups, Geometry and Physics (ed Clemente-Gallardo and Martinez) Monografia 29, Real Academia de Ciencias de Zaragoza (2007) 79-92.

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M. Crampin, Kähler and para-Kähler structures associated with Finsler spaces of non-zero constant flag curvature. Houston J. Math. 34 (2008) 99-114.

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M. Crampin and D.J. Saunders, Fefferman-type metrics and the projective geometry of sprays in two dimensions. Math. Proc. Cam. Phil. Soc. 142 (2007) 509-523.

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M. Crampin and D.J. Saunders, Path geometries and almost Grassmann structures. Adv. Stud. Pure Math. 48 (2007) 225-261.

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M. Crampin, On the inverse problem for sprays. Publ. Math. (Debrecen) 70 (2007) 319-335.

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M. Crampin, Isotropic and R-flat sprays. Houston J. Math.33 (2007) 451-459.

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M. Crampin, On the orthogonal separation of variables in the Hamilton-Jacobi equation for geodesics in a Riemannian manifold. Differential Geometry and its Applications (Proceedings of the 9th
International Conference, Prague 2004); ed. Bures, Kowalski, Krupka, Slovak; matfyzpress, Prague, 2005; 453-466.

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M. Crampin and D.J. Saunders, Affine and projective transformations of Berwald connections. Diff. Geom. Appl. 25 (2007) 235-250.

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M. Crampin and D.J. Saunders, Projective connections. J. Geom. Phys. 57 (2007) 691-727.

ScienceDirect: 10.1016/j.geomphys.2006.03.007

M. Crampin and D.J. Saunders, On projective connections: the general case. Unpublished (2004).

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M. Crampin and D.J. Saunders, On projective connections: the affine case. Unpublished (2004).

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M. Crampin and D.J. Saunders, Cartan’s concept of duality for second-order ordinary differential equations. J. Geom. Phys. 54 (2005) 146-172

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M. Crampin,
Randers spaces with reversible geodesics. Publ. Math. (Debrecen) 67 (2005) 401-409.

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M. Crampin,
The second-order ordinary differential equation: Cartan, Douglas, Berwald. Periodica Mathematica
Hungarica 48 (2004) 151-164.

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M. Crampin and D. J. Saunders,
On null Lagrangians. Diff. Geom. Appl. 22 (2005) 131-146.

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M. Crampin,
Projectively equivalent Riemannian spaces as quasi-bi-Hamiltonian
systems,
Acta Appl. Math. 77 (2003) 237-248.

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M. Crampin,
Gaussian curvature as a null homogeneous second-order Lagrangian,
Publ. Math. (Debrecen) 62 (2003) 351-361.

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M. Crampin and D. J. Saunders,
The Hilbert-Caratheodory and Poincare-Cartan forms for higher-order
multiple-integral variational problems,
Houston J. Math. 30 (2004) 657-689.

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M. Crampin and D. J. Saunders,
The Hilbert-Caratheodory form for parametric multiple integral
problems in
the calculus of variations,
Acta Applicandae Math. 76 (2003) 37-55.

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M. Crampin,
Conformal Killing tensors with vanishing torsion and the
separation of variables in the Hamilton-Jacobi equation,
Diff. Geom. Appl. 18 (2002) 87-102.

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M. Crampin,
The curvature of a curve and variational calculus,
Publ. Math. (Debrecen) 59 (2001) 429-439.

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D. J. Saunders and M. Crampin, Variational problems on Lie algebroids, Diff. Geom. Appl. 15 (2001) 165-174.

M. Crampin,
The Morse index theorem for general end conditions,
Houston J., Math. 27 (2001) 807-822.

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M. Crampin,
On the inverse problem of the calculus of variations for
systems of second-order ordinary differential equations.
In: Finslerian Geometries ed. Antonelli Kluwer (2000) 139-150.

M. Crampin,
Connections of Berwald type,
Publ. Math. (Debrecen) 57 (2000) 455-473.

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M. Crampin,
The second variation formula in Lagrange and Finsler geometry,
Houston J. Math. 26 (2000) 255-276.

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