Dr Yuri

Dr Yuri Nikolayevsky

Senior Lecturer

College of Science, Health and Engineering

School of Engineering and Mathematical Sciences

Department of Mathematics and Statistics

Physical Sciences 2, Room 219, Melbourne (Bundoora)

Qualifications

MSc (Kharkov), PhD (Leningrad)

Role

Academic

Membership of professional associations

AustMS

Area of study

Mathematics and Statistics

Brief profile

My mathematical interests are:

  • Riemannian and differential geometry
  • Geometry of Lie groups and homogeneous spaces
  • Topological graph theory

Teaching units

MAT1NLA Number systems and Linear Algebra

MAT3AC Advanced Calculus and Curvature

MAT2ANA Analysis of Real Numbers and Functions

MAT4TOP Topology

Recent publications

with V.Matveev, Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties. Ann. Inst. Fourier.

with G.Cairns, A.Hinić Galić, Curvature properties of metric nilpotent Lie algebras which are independent of metric. Ann. Global Anal. Geom.

with I.Tsartsaflis, Cohomology of ℕ-graded Lie algebras of maximal class over ℤ2. J. Lie Theory. 27 (2017), 529 – 544.

with J.H.Park, H-contact unit tangent sphere bundles of Riemannian manifolds. Diff. Geom. Appl. 49 (2016) 301 – 311.

with Z.Rakić, The Duality principle for Osserman algebraic curvature tensors. Linear Algebra Appl. 504 (2016), 574 – 580.

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.

with G.Cairns, G.Rossiter, Conewise linear periodic maps of the plane with integer coefficients. Amer. Math. Monthly, 123 (2016), 363 – 375.

Solvable extensions of negative Ricci curvature of filiform Lie groups. Math. Nachr. 289 (2016), 321 – 331.

with G.Cairns, T.Koussas, Spherical Thrackles. Discrete Math. 338 (2015), 2507 – 2513.

with V.Matveev, A counterexample to Belgun-Moroianu conjecture. C.R. Acad. Sci. Paris Sér. I Math. 353 (2015), 455 – 457.

Totally geodesic hypersurfaces of homogeneous spaces. Israel J. Math. 207 (2015), 361 – 375.

with Yu.Nikonorov, Solvable Lie groups of negative Ricci curvature. Math. Z. 280 (2015), 1 – 16.

with G.Cairns, A.Hinić Galić, I.Tsartsaflis, Geodesic bases for Lie algebras. Linear Multilinear Algebra 63 (2015), 1176 – 1194.

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. 

Weyl-Schouten Theorem for symmetric spaces. Proc. London Math. Soc. 107 (2013), 151 – 176.

with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of filiform nilpotent Lie algebras. J. Lie Theory, 23 (2013), 1051 – 1074. 

with G.Cairns, A.Hinić Galić, Totally geodesic subalgebras of nilpotent Lie algebras. J. Lie Theory, 23 (2013), 1023 – 1049. 

Conformally Osserman manifolds of dimension 16 and Weyl-Schouten Theorem for rank-one symmetric spaces. Ann. Mat. Pura Appl. 191 (2012), 677 – 709.

Einstein solvmanifolds attached to two-step nilradicals. Math.Z. 272 (2012), 675 – 695.

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.

Weyl homogeneous manifolds modelled on compact Lie groups. Diff. Geom. Appl. 28 (2010) 689 – 696.

Conformally Osserman manifolds. Pacific J. Math. 245 (2010), 315 – 358.

with G.Cairns, Generalized Thrackle Drawings of Non-Bipartite Graphs. Discrete Comput. Geom. 41 (2009), 119 – 134.

Older publications

Research projects

La Trobe Asia 2015 Homogeneous geometric structures from the viewpoint of Submanifold geometry

ARC 2013 – 2015 Symmetries in real and complex geometry

DGS 2013 Real Geometry (joint with Grant Cairns)

DGS 2012 Curvature Homogeneous spaces modelled on group manifolds

DGS 2011 Conformal relatives of symmetric spaces

DGS 2010 Conformally Osserman manifolds