astronomy

Ravindra Shripad Kulkarni

Ravindra Shripad Kulkarni is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ravindra Shripad Kulkarni rather than just read about it. In short: Ravindra Shripad Kulkarni (born 1942) is an Indian mathematician, specializing in differential geometry. He is known for the Kulkarni–Nomizu product.

Key takeaways

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Reference excerpt

Ravindra Shripad Kulkarni (born 1942) is an Indian mathematician, specializing in differential geometry. He is known for the Kulkarni–Nomizu product.

Education and career Ravi S. Kulkarni received in 1968 his Ph.D. from Harvard University under Shlomo Sternberg with thesis Curvature and Metric. For the academic year 1980–1981 he was a Guggenheim Fellow.

After a research and teaching career spanning over 40 years in the US at Johns Hopkins University, Columbia University, Indiana University Bloomington, Queens College of the City University of New York and the Graduate Center of the City University of New York. He returned to India as Distinguished Professor and Director of Harish-Chandra Research Institute, one of three research institutes for Mathematics and Theoretical Physics in India, followed by a 7-year stint at the Indian Institute of Technology Bombay as Mathematics Chair. He is interested in the philosophy of Mathematics and Science, and notes he has “…not yet figured out the enigma of how Ramanujan’s mind worked”. He has served as the president of the Ramanujan Mathematical Society.

Selected publications Kulkarni, Ravindra S. (1969). "Curvature structures and conformal transformations". Bulletin of the American Mathematical Society. 75: 91–94. doi:10.1090/s0002-9904-1969-12155-5. MR 0233306. Kulkarni RS (1972). "Conformally Flat Manifolds". Proceedings of the National Academy of Sciences. 69 (9): 2675–2676. Bibcode:1972PNAS...69.2675K. doi:10.1073/pnas.69.9.2675. PMC 427014. PMID 16592016. Kulkarni RS (1975). "On complexification of real manifolds". Proceedings of the National Academy of Sciences. 72 (11): 4210. Bibcode:1975PNAS...72.4210K. doi:10.1073/pnas.72.11.4210. PMC 388688. PMID 16592283. Kulkarni, R. S. (1975). "A finite version of Schur's theorem". Proceedings of the American Mathematical Society. 53 (2): 440–442. doi:10.1090/s0002-9939-1975-0383295-8. MR 0383295. Kulkarni, R. S. (1975). "Conformal geometry in higher dimensions. I." Bulletin of the American Mathematical Society. 81 (4): 736–738. doi:10.1090/s0002-9904-1975-13847-x. MR 0417980. Kulkarni, R. S. (1980). "On Hurwitz' "84(g – 1) theorem" and pseudofree actions". Bulletin of the American Mathematical Society. 2 (2): 303–305. doi:10.1090/s0273-0979-1980-14743-6. MR 0555267. with Allan L. Edmonds & John H. Ewing: Edmonds, Allan L.; Ewing, John H.; Kulkarni, Ravi S. (1986). "Torsion free subgroups of Fuchsian groups and tessellations of surfaces". Bulletin of the American Mathematical Society. 6 (3): 456–458. doi:10.1090/s0273-0979-1982-15014-5. MR 0648534. with Allan L. Edmonds & Robert E. Stong: Edmonds, Allan L.; Kulkarni, Ravi S.; Stong, Robert E. (1984). "Realizability of branched coverings of surfaces". Transactions of the American Mathematical Society. 282 (2): 773–790. doi:10.1090/s0002-9947-1984-0732119-5. MR 0732119. with Gregory Constantine: Constantine, Gregory; Kulkarni, Ravi S. (1984). "On a result of S. Delsarte". Proceedings of the American Mathematical Society. 92: 149–152. doi:10.1090/s0002-9939-1984-0749907-7. MR 0749907. with Hyman Bass: Bass, Hyman; Kulkarni, Ravi (1990). "On uniform tree lattices". Journal of the American Mathematical Society. 3 (4): 843–902. doi:10.1090/s0894-0347-1990-1065928-2. MR 1065928. Kulkarni, Ravi S. (1997). "Riemann surfaces admitting large automorphism groups". Extremal Riemann surfaces (San Francisco, California, 1995). Contemporary Mathematics. Vol. 201. Providence, Rhode Island: American Mathematical Society. pp. 63–79. doi:10.1090/conm/201/02610. ISBN 978-0-8218-0514-5. MR 1429195. with Krishnendu Gongopadhyay: Gongopadhyay, Krishnendu; Kulkarni, Ravi S. (2009). "z-classes of isometries of the hyperbolic space". Conformal Geometry and Dynamics. 13 (4): 91–109. arXiv:0707.0487. Bibcode:2009CGDAM..13...91G. doi:10.1090/s1088-4173-09-00190-8. MR 2491719. S2CID 13568444.

as editor with Ulrich Pinkall: Conformal geometry. Aspects of Mathematics (proceedings of a seminar on conformal geometry at the Max-Planck Institute in 1985–1986). Braunsweig & Wiesbaden: Friedr. Vieweg & Sohn. 1988.

References

External links Conformal Geometry and Riemann Surfaces: A Conference in Honor of Professor Ravi S. Kulkarni, posted 28 October 2013

Worked examples

Example 1 — a first encounter with Ravindra Shripad Kulkarni

Start with the simplest possible case. Write down what Ravindra Shripad Kulkarni claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ravindra Shripad Kulkarni before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ravindra Shripad Kulkarni ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ravindra Shripad Kulkarni

In research: Ravindra Shripad Kulkarni appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Ravindra Shripad Kulkarni in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Ravindra Shripad Kulkarni is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 20th-century Indian mathematicians, 21st-century Indian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ravindra Shripad Kulkarni outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

What is Ravindra Shripad Kulkarni in simple terms?

Ravindra Shripad Kulkarni (born 1942) is an Indian mathematician, specializing in differential geometry. He is known for the Kulkarni–Nomizu product.

Why does Ravindra Shripad Kulkarni matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ravindra Shripad Kulkarni?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ravindra Shripad Kulkarni.