La Trobe Mathematics and Statistics Official Home Page
Office: Room 217, Physical Sciences 2 Address: Department of Mathematics and Physics, La Trobe University, Melbourne, Victoria 3086, Australia Phone: +61 (03) 9479 1644 Email:
Research interests - Lie groups and Lie algebras, homogeneous spaces and symmetric spaces.
- Riemannian geometry, geometry of submanifolds, integral and conformal geometry.
- Topological graph theory.
Looking for a PhD supervisor?
Contact me. General information: Postgraduate studies at La Trobe University.
Publications and preprints - with J.A.Wolf, The Structure of Geodesic Orbit Lorentz Nilmanifolds. (preprint)
- with G.Cairns, Respectful decompositions of Lie algebras. (preprint)
- with An Ky Nguyen, Stability of geodesic vectors in low-dimensional Lie algebras. (preprint)
- with J.H.Park, Einstein hypersurfaces in irreducible symmetric spaces. (preprint)
- with Y.Euh, J.Kim, J.H.Park, On 2-stein submanifolds in space forms. Results Math. 77 (2022), 84, doi: 10.1007/s00025-022-01620-9 (preprint)
- with S.Kim, J.H.Park, Einstein hypersurfaces of Damek-Ricci spaces. J. Geom. Phys. 167 (2021), 104278, doi: 10.1016/j.geomphys.2021.104278. (preprint)
- with Z. Chen, Yu. Nikonorov, Compact geodesic orbit spaces with a simple isotropy group. (preprint)
- O.Dearricott, W.Tuschmann, Y.Nikolayevsky, T.Leistner, D.Crowley (Eds.) Differential Geometry in the Large (London Mathematical Society Lecture Note Series). Cambridge: Cambridge University Press, 463 (2020).
- with G.Cairns, B.Jessup, A class of nilpotent Lie algebras whose center acts nontrivially in cohomology. Proc. Amer. Math. Soc. 148 (2020), 1945-1952. (preprint)
- with G.Cairns, E.Groves, Bad drawings of small complete graphs. Australas. J. Comb. 75(3) (2019), 322-342. (preprint)
- with S.Kim, J.H.Park, Einstein hypersurfaces of the Cayley projective plane. Diff. Geom. Appl. 69 (2020), doi: 10.1016/j.difgeo.2020.101594. (preprint)
- with S.Kim, J.H.Park, Totally geodesic submanifolds of Damek-Ricci spaces. Rev. Mat. Iberoam. 37 (2021), 1321-1332, doi: 10.4171/rmi/1228. (preprint)
- with D.Alekseevsky, Einstein extensions of Riemannian manifolds. Trans. Amer. Math. Soc. 374 (2021), 6059-6083. (preprint)
- Geodesic orbit and naturally reductive nilmanifolds associated with graphs. Math. Nachr. 293 (2020), 754-760. (preprint)
- with A.Borisenko, On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space. J. Geom. Phys. 155 (2020), doi: 10.1016/j.geomphys.2020.103776. (preprint)
- with P.Adams, Planar bipartite biregular degree sequences. Discrete Math. 342 (2019), 433-440. (preprint)
- with G.Misereh, Annular and pants thrackles. Discrete Math. Theor. Comput. Sci. 20:1 (2018), #16, 17 pp.
- with Yu.Nikonorov, On invariant Riemannian metrics on Ledger-Obata spaces. manuscripta math. 158 (2019), 353-370. (preprint)
- with W.Globke, Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension. Diff. Geom. Appl. 54B (2017), 475-489. (preprint)
- with G.Misereh, Thrackles containing a standard musquash. Australas. J. Comb. 70 (2018), 168–184. (preprint)
- with V.Matveev, Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties. Ann. Inst. Fourier, 67 (2017), 843-862. (preprint)
- with G.Cairns, A.Hinić Galić, Curvature properties of metric nilpotent Lie algebras which are independent of metric. Ann. Global Anal. Geom. 51 (2017), 305-325. (preprint)
- with I.Tsartsaflis, Cohomology of ℕ-graded Lie algebras of maximal class over ℤ2. J. Lie Theory, 27 (2017), 529-544. (preprint)
- with J.H.Park, H-contact unit tangent sphere bundles of Riemannian manifolds. Diff. Geom. Appl. 49 (2016), 301–311. (preprint)
- with Z.Rakić, The Duality principle for Osserman algebraic curvature tensors. Linear Algebra Appl. 504 (2016), 574-580. (preprint)
- with G.Cairns, S.Mendan, A sufficient condition for a pair of sequences to be bipartite graphic. Bull. Austral. Math. Soc. 94 (2016), 195-200. (preprint)
- with G.Cairns, G.Rossiter, Conewise linear periodic maps of the plane with integer coefficients. Amer. Math. Monthly, 123 (2016), 363-375. (preprint)
- Solvable extensions of negative Ricci curvature of filiform Lie groups. Math. Nachr. 289 (2016), 321-331. (preprint)
- with G.Cairns, T.Koussas, Great-circle spherical Thrackles. Discrete Math. 338 (2015), 2507-2513. (preprint)
- with V.Matveev, A counterexample to Belgun-Moroianu conjecture. C.R. Acad. Sci. Paris Sér. I Math. 353 (2015), 455–457. (preprint)
- Totally geodesic hypersurfaces of homogeneous spaces. Israel J. Math. 207 (2015), 361-375. (preprint)
- with Yu.Nikonorov, Solvable Lie groups of negative Ricci curvature. Math. Z. 280 (2015), 1-16. (preprint)
- with G.Cairns, A.Hinić Galić, I.Tsartsaflis, Geodesic bases for Lie algebras. Linear Multilinear Algebra, 63 (2015), 1176-1194. (preprint)
- with G.Cairns, S.Mendan, A sharp refinement of a result of Zverovich - Zverovich. Discrete Math. 338 (2015), 1085-1089.
(preprint)
- with G.Cairns, S.Mendan, A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences. Australas. J. Combin. 60 (2014), 217-226. (preprint)
- with G.Cairns, N.T.Tung Le, A.Nielsen, On the existence of orthonormal geodesic bases for Lie algebras. Note Mat. 33 (2013), 11-18. (preprint)
- with Z.Rakić, A note on Rakić duality principle for Osserman manifolds. Proc. 17 Geom. Seminar Zlatibor, 2012. Publ. Inst. Math., Nouv. Ser. 94 (108) (2013), 43-45. (preprint)
- Weyl-Schouten Theorem for symmetric spaces. Proc. London Math. Soc. 107 (2013), 151-176. (preprint)
- with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of filiform nilpotent Lie algebras. J. Lie Theory, 23 (2013), 1051-1074. (preprint)
- with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of nilpotent Lie algebras. J. Lie Theory, 23 (2013), 1023-1049. (preprint)
- Einstein solvmanifolds attached to two-step nilradicals. Math. Z. 272 (2012), 675-695. (preprint)
- Conformally Osserman manifolds of dimension 16 and Weyl-Schouten Theorem for rank-one symmetric spaces. Ann. Mat. Pura Appl. 191 (2012), 677-709. (preprint)
- with G.Cairns, Outerplanar Thrackles. Graphs Combin. 28 (2012), 85-96.
- Einstein solvmanifolds and the pre-Einstein derivation. Trans. Amer. Math. Soc. 363 (2011), 3935-3958. (preprint)
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Totally umbilical submanifolds in G(2,n). IV. Math. Fiz. Anal. Geom. 5 (1998), 95 -113. (читать по-русски)
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Totally umbilical submanifolds in G(2,n). III. Math. Fiz. Anal. Geom. 3 (1996), 339 -355. (читать по-русски)
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On Fenchel's problem. Mat. Zametki 56 (1994), 87 – 97; translation in Math. Notes 56 (1994), 1158 -1164.
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Submanifolds of Euclidean space with a totally geodesic Gauss image. Dokl. Akad. Nauk SSSR 314 (1990), 297-300; translation in Soviet Math. Dokl. 42 (1991), 456-459.
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