Papers by Ravindra Kulkarni
Bulletin of the American Mathematical Society, 1980
Bookmarks Related papers MentionsView impact
arXiv (Cornell University), 2009
Let G be a group. Two elements x,y are said to be in the same z-class if their centralizers are c... more Let G be a group. Two elements x,y are said to be in the same z-class if their centralizers are conjugate in G. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a non-degenerate symmetric, or skew-symmetric, bilinear form on V. Let I(V, B) denote the group of isometries of (V, B). We show that the number of z-classes in I(V, B) is finite when F is perfect and has the property that it has only finitely many field extensions of degree at most n.
Bookmarks Related papers MentionsView impact
arXiv (Cornell University), Nov 17, 2005
Bookmarks Related papers MentionsView impact
arXiv (Cornell University), Dec 20, 2020
Bookmarks Related papers MentionsView impact
Proceedings - Mathematical Sciences, 2018
Bookmarks Related papers MentionsView impact
Bulletin of the American Mathematical Society, 1975
Bookmarks Related papers MentionsView impact
Journal of Differential Geometry, 1978
Bookmarks Related papers MentionsView impact
Journal of Differential Geometry, 1985
Bookmarks Related papers MentionsView impact
Linear Algebra and its Applications, 2011
Bookmarks Related papers MentionsView impact
Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1991
Bookmarks Related papers MentionsView impact
Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1991
Bookmarks Related papers MentionsView impact
Transactions of the American Mathematical Society, 1984
A branched covering M → N M \to N of degree d d between closed surfaces determines a collection D... more A branched covering M → N M \to N of degree d d between closed surfaces determines a collection D \mathfrak {D} of partitions of d d —its "branch data"—corresponding to the set of branch points. The collection of partitions must satisfy certain obvious conditions implied by the Riemann-Hurwitz formula. This paper investigates the extent to which any such finite collection D \mathfrak {D} of partitions of d d can be realized as the branch data of a suitable branched covering. If N N is not the 2 2 -sphere, such data can always be realized. If D \mathfrak {D} contains sufficiently many elements compared to d d , then it can be realized. And whenever d d is nonprime, examples are constructed of nonrealizable data.
Bookmarks Related papers MentionsView impact
Topology, 1987
Bookmarks Related papers MentionsView impact
Asian Journal of Mathematics, 2008
Bookmarks Related papers MentionsView impact
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985
The classical Riemann mapping theorem essentially says that a simply connected two-dimensional sm... more The classical Riemann mapping theorem essentially says that a simply connected two-dimensional smooth Riemannian manifold is conformal to the standard sphere S 2 , the Euclidean plane E 2 , or the unit disk D 2 . The analogous problems in the Lorentz case are as follows. Let M be a simply connected two-dimensional smooth Lorentz manifold. Note that necessarily M is diffeomorphic to R 2 . (1) Does M admit a conformal embedding in E 1, 1 ,i.e. R 2 with cartesian coordinates { x, y } and the metric d x d y ? (2) What are the conformal types of such M’s ? In this paper these questions are partly answered in terms of an ‘ ideal boundary’ ∂ 0 M which is a conformal invariant of M. A geometric consequence is that among orientable surfaces only R 2 , R x S 1 and S 1 x S 1 admit complete Lorentz metrics of constant curvature. The results of this paper may be regarded as a part of a global study of space-times as well as of the second-order linear hyperbolic operators in dimension 2.
Bookmarks Related papers MentionsView impact
Proceedings of the National Academy of Sciences, 1975
This paper studies the problem of obtaining complexifications of a differentiable manifold which ... more This paper studies the problem of obtaining complexifications of a differentiable manifold which have desirable analytic or algebraic properties and which are minimal in the sense described below. It is seen that there is a significant difference between analytic and algebraic complexifications.
Bookmarks Related papers MentionsView impact
Proceedings of the American Mathematical Society, 1984
For an isomorphism type of a finite abelian p p -group X X it is shown that the matrix ( p ⟨ s ( ... more For an isomorphism type of a finite abelian p p -group X X it is shown that the matrix ( p ⟨ s ( D ) , s ( Y ) ⟩ ) ({p^{\left \langle {s(D),s(Y)} \right \rangle }}) is nonsingular; D D , Y ∈ { S | S ⩽ X and S ≠ X } Y \in \left \{ {S|S \leqslant X\;{\text {and}}\;S \ne X} \right \} , the set of all proper isomorphism type of subgroups of X X . Here s ( Y ) s(Y) denotes the signature of Y Y . This completes the proof of a result of S {\text {S}} . Delsarte which gives explicit formulas for the number of automorphisms of X X , the number of subgroups of X X isomorphic to Y Y (and the number of homomorphisms from Y Y into X X ) in terms of signatures.
Bookmarks Related papers MentionsView impact
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989
A Neumann subgroup of the classical modular group is by definition a complement of a maximal para... more A Neumann subgroup of the classical modular group is by definition a complement of a maximal parabolic subgroup. Recently Neumann subgroups have been studied in a series of papers by Brenner and Lyndon. There is a natural extension of the notion of a Neumann subgroup in the context of any finitely generated Fuchsian group Γ acting on the hyperbolic plane H such that Γ/H is homeomorphic to an open disk. Using a new geometric method we extend the work of Brenner and Lyndon in this more general context.
Bookmarks Related papers MentionsView impact
Journal of the American Mathematical Society, 1990
Bookmarks Related papers MentionsView impact
International Journal of Mathematics and Mathematical Sciences, 1978
It is shown that (i) a diffeomorphism of manifolds with indefinite metrics preserving degenerater... more It is shown that (i) a diffeomorphism of manifolds with indefinite metrics preserving degenerater-plane sections is conformal, (ii) a sectional curvature-preservlng diffeomorphism of manifolds with indefinite metrics of dimension≥4is generically an isometry.
Bookmarks Related papers MentionsView impact
Uploads
Papers by Ravindra Kulkarni