Frank Klinker


Papers

  • Approximation of D.I.Y. water rocket dynamics including air drag. Int. J. of Sci. Research in Mathematical and Statistical Sciences 6 (2019) no. 6, 1-13. Joint Work with L. Fischer, T. Günther, L. Herzig, T. Jarzina, S. Knipper, F.-G. Schürmann, M. Wollek (Journal or arXiv)
  • On the characterization of the degree of interpolation polynomials in terms of certain combinatorical matrices. Arab. J. Math. 8 (2019) no. 1, 55-62. Joint work with C. Reineke (Journal or arXiv)
  • On the regularity of matrices with uniform polynomial entries. São Paulo J. Math. Sci. 13 (2019) no. 1, 370-379. Joint work with C. Reineke (Journal or arXiv)
  • The general non-symmetric, unbalanced star circuit: On the geometrization of problems in electrical measurement. Math. Semesterber. 64 (2017) no. 1, 25-39. Joint work with R. Gäer, Schniewindt GmbH & Co. KG, and C. Eggert, ThyssenKrupp Rothe Erde GmbH (Journal or arXiv)
  • An explicit description of SL(2,C) in terms of SO+(3,1) and vice versa. Int. Electron. J. Geom. 8 (2015) no. 1, 94-104 (Journal or arXiv)
  • Eleven-dimensional symmetric supergravity backgrounds, their geometric superalgebras, and a common reduction. Bulg. J. Phys. 41 (2014) no. 2, 130-141 (Journal or arXiv)
  • A family of non-restricted D=11 geometric supersymmetries. J. Geom. Phys. 86 (2014) 534-553 (Journal or arXiv)
  • Connections on Cahen-Wallach spaces. Adv. Appl. Clifford Algebr. 24 (2014) no. 3, 737-768 (Journal or arXiv)
  • Ein optimiertes Glättungsverfahren motiviert durch eine technische Fragestellung (An optimized smoothing method motivated by a technical problem). Math. Semesterber. 59 (2012) no. 1, 29-55, German. Joint work with G. Skoruppa, in cooperation with W. Kranz, Kranz Software Engineering (Journal or arXiv)
  • Generalized duality for k-forms. J. Geom. Phys. 61 (2011) no. 12, 2293-2308 (Journal or arXiv)
  • Exponential Moving Average versus Moving Exponential Average. Math. Semesterber. 58 (2011) no. 1, 97-107. In cooperation with S. Pohlschröder (Journal or arXiv)
  • Polynomial poly-vector fields. Int. Electron. J. Geom. 2 (2009) no. 1, 55-73 (Journal or arXiv).
    Appendix: Quadratic Poisson structures in dimension four. 2008, 22 pp (pdf)
  • SUSY structures on deformed supermanifolds. Differential Geom. Appl. 26 (2008) no. 5, 566-582 (Journal or arXiv)
  • The decomposition of the spinor bundle of Grassmann manifolds. J. Math. Phys. 48 (2007) no. 11, 113511, 26 pp (Journal or arXiv)
  • The torsion of spinor connections and related structures. SIGMA, Symmetry Integrability Geom. Methods Appl. 2 (2006) Paper 077, 28 pp (Journal or arXiv)
  • Supersymmetric Killing structures. Comm. Math. Phys., 255 (2005) no. 2, 419-467 (Journal or arXiv)

Preprints / Non-refereed Papers

  • Die Keplersche Fassregel und Numerische Quadraturverfahren (The Keplersche Fassregel and numerical quadrature). 2010, 28 pp (pdf, German); A preprint of sections 1+2 has been published in Mathematik-Seminar des Freistaates Sachsen, Heft Sayda, Leipzig, 2001.
  • Quadratic Poisson structures in dimension four. Appendix to "Polynomial poly-vector fields". 2008, 22 pp (pdf)
  • The signs. Appendix to "Supersymmetric Killing structures". 2003, 4 pp. (pdf)
  • The spinor bundle of Riemannian products. arXiv:math.DG/0212058, 2002, 7 pp (arXiv)

Theses

  • Supersymmetric extensions of solvable Lorentzian symmetric spaces. Habilitation thesis, TU Dortmund University, 2013, 112 pp (Abstract/Summary).
  • Supersymmetric Killing structures. Doctoral thesis, Leipzig University, 2003, 116 pp (DNB entry)
  • Zusammenhänge auf Prinzipalbündeln und Instantonen auf S⁴ (Connections on Principal Bundles and Instantons on S⁴). Diploma thesis, University of Osnabrück, 2000, 104 pp (pdf, German)

Lecture Notes

  • Grundlagen der Kartographie (Elementary Cartography). Lecture notes, 2019, 115+ pp (German) - in progress,
  • Grundlagen der Analysis: Ein dreisemestriger Kurs (Elementary Analysis: A Three-Term Course). Lecture notes, 2016/2018, 343 pp (pdf, German)
  • Differentialgeometrie I: Kurven und Flächen (Differential Geometry I: Curves and Surfaces). Lecture notes, 2014/2016, 130 pp (pdf, German)
  • Mathematischer Vorkurs (Preliminary course in mathematics). Lecture notes, 2012, 105 pp (pdf, German)
  • The Kontsevitch quantization formula. Notes from Talk given at a joint seminar of the groups Differential Geometry and Theoretical Physics III, TU Dortmund, 2004, 14 pp. (pdf)
  • Lineare Algebra auf Räumen mit anti-kommutierenden Koeffizienten (Linear algebra on spaces with anti-commuting coefficients). 2001, 29 pp (pdf, German)

Teaching material

  • Material für den Mathematik- und Physikunterricht (Teaching material for math and physics classes), since 2019 (here, German)
  • Spurfreie Matrizen als Kommutatoren (Trace free matrices as commutators). 2011, 9 pp. (pdf, German)
  • Die Gaußsche Gerade (The Gauß line). 2011, 4 pp. (pdf, German)
  • Ein effizientes Verfahren zur simultanen Berechnung einer Basis von Summe und Schnitt zweier Vektorräume (An efficient way to calculate a basis of the sum and intersection of two vector spaces). 2008, 4 pp. (pdf, German)