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Professional Homepage for

 Jeffrey M. Lee
Associate Professor of Mathematics

Texas Tech University Department of Mathematics and Statistics

Email: My email is of the form firstname.lastname@ttu.edu but be sure to use "jeffrey" rather than "jeff" or you will be emailing the other Jeffrey Lee who works in the Geography department.

Office Location: Room 239 in the Mathematics Building

Research Interests: Differential Geometry, Mathematical Physics, Spectral Geometry.

I am working on a differential geometry book. The link to the PDF version is below together with an extensive online supplement and the beginnings of a second volume. You are free to download it but not to distribute it without the author's permission. What I ask in return is that you take note of mistakes etc. and notify me of such by email (see above). Please do not put any of this material on a different website! The material below (the  book, the online supplement, and the nascent second volume book II) are the copyrighted. You may not claim authorship of any of this material (in part or whole) or modify any of the contents without express permission  of the author. 

Manifolds and Differential Geometry  (latest version--1/29/2009)

Update: The Book below is scheduled to be published by the AMS and is no longer available here.

Online Supplement to "Manifolds and Differential Geometry".(latest version--5/4/2009) Added: symplectic geometry, and connections on principal bundles (Supp to Chap. 12) and alternate proof of flat test case  (Supp. to Chap. 13)

(Thanks to readers Efton Park, Ken Richardson, Greg Friedman, Lance Drager, Igor Prokhorenkov, and David Weinberg. Also thanks to David Bleecker for kind comments and for fixing the file so that the book pagination and the PDF pagination match)

There is also a short (3 or 4 pages) primer on manifolds: HERE.

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some notes

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Selected Publications (not quite in chronological order)

1. Drager, Lance D.; Lee, Jeffrey M.; Martin, Clyde F. On the geometry of the smallest circle enclosing a finite set of points. J. Franklin Inst. 344 (2007), no. 7, 929--940. 51M04 (68U05)

2. (with L. Drager and R. Byerly) Observability of Finite Dynamical Systems, IEEE Transactions on Information Theory,  (2003)

3.  (with Ken Richardson) Lichnerowicz and Obata Theorems for foliations, Pacific Journal of Mathematics, vol. 206, no. 2, 339-357 (2002).

4. Lee, Jeffrey M.; Richardson, Ken Riemannian foliations and eigenvalue comparison. Ann. Global Anal. Geom. 16 (1998), no. 6, 497--525. (Reviewer: James F. Glazebrook) 53C12 (58G25)

6. Geometry detected by a finite part of the spectrum. Progress in inverse spectral geometry, 15--22, Trends Math., Birkhäuser, Basel, 1997. (Reviewer: Ruth Gornet) 58J50 (58J53)

7. Dimension, volume, and spectrum of a Riemannian manifold. Illinois J. Math. 37 (1993), no. 1, 14--32.

8. Finite inverse spectral geometry. Geometry and nonlinear partial differential equations (Fayetteville, AR, 1990), 85--100, Contemp. Math., 127, Amer. Math. Soc., Providence, RI, 1992.

9. (with Harold Donnelly) Domains in Riemannian Manifolds and Inverse Spectral Geometry, Pacific Journal of Mathematics, Vol. 150, No. 1 (1991).

10. Donnelly, Harold; Lee, Jeffrey Heat kernel remainders and inverse spectral theory. Illinois J. Math. 35 (1991), no. 2, 316--330

11. Eigenvalue comparison for tubular domains. Proc. Amer. Math. Soc. 109 (1990), no. 3, 843--848.

12. The gaps in the spectrum of the Laplace-Beltrami operator. Houston J. Math. 17 (1991), no. 1, 1--24.

13. Hearing the volume of a drum in hyperbolic space. Indiana Univ. Math. J. 39 (1990), no. 3, 585--615

More:

14. Mao, Yiping; Lee, Jeffrey Two-point boundary value problems for nonlinear differential equations. Rocky Mountain J. Math. 26 (1996), no. 4, 1499--1515

15. Lee, Jeffrey M.; Weinberg, David A. A note on canonical forms for matrix congruence. Linear Algebra Appl. 249 (1996), 207--215.

16. Lee, Jeffrey; Page, Robert; Pantrangenaru, Vic, Ruymgaart, F. Nonparametric density estimation on homogeneous spaces in high level image analysis analysis, Bioinformatics, Images and Wavlets; Program and Abstracts. Aykroyd, Barber and Mardia Eds. pp 37-40 http://www.amsta.leeds.ac.uk/Statistics/workshop/lasr2004/Proceedings/paige.pdf

Some Graduate Courses Taught

Institution: Texas Tech University

Mathematics 4331

Year 1999 First summer session

Mathematics 5342

Year 2000  Fall

Mathematics 5343

Year 2001  Spring

Mathematics 5310

Year 2001 Fall

Mathematics 5311

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