Selected Bibliography

Riemannian Submanifolds

Selected Bibliography

gathered by Charles E. Snygg

S. Alexander

Reducibility of Euclidean immersions of low codimension, J. of Diff. Geom. 3(1969), 69-82.

W. Ambrose

Parallel translation of Riemannian curvature, Ann. of Math. (2) 64 (1956), 337-363. MR 21 1627 (footnote 1).

R.L. Bishop and R.J. Crittenden

Geometry of Manifolds, Pure and Appi. Math. XV, Acad. Press, New York, 1964. MR 29 6401.

S.S. Chern

Minimal Submanifolds in a Riemannian Manifold, Tech. Rep. 19 (N.S.), Univ. of Kansas, Lawrence, 1968. Referred to in MR 38 1617.

E. A. Coddington and N. Levinson

Theory of Ordinary Differential Equations, International Ser. in Pure and Appi. Math., McGraw-Hill, New York, 1955. MR 16 1022.

L.P. Eisenhart

Riemannian Geometry, rev. ed., Princeton Univ. Press, Princeton, 1949. MR 11 687.

A. Fialkow

Hypersurfaces of a space of constant curvature, Ann. of Math. (2) 39 (1938), 762-785. (footnote 3)

H.M. Flanders

Differential Forms with Applications to the Physical Sciences, Acad. Press, New York, 1963. MR 28 5397.

N.J. Hicks

[1] A theorem on affine connexions, Illinois J. of Math. 3(1959), 242-254. MR 21 6597.

[2] Submanifolds of semi-Riemannian manifolds, Rend. Circ. Mat. Palermo 12 (1963), 137-149. MR 29 1601.

[3] Notes on Differential Geometry, Van Nostrand Math. Studies 3, Van Nostrand, Princeton, 1965. MR 31 3936.

[4] Connexion preserving spray maps, Illinois J. of Math. 10 (1966), 661-679. MR 34 5024.

N. Jacobson

Linear Algebra, Lectures in Abstract Algebra II, Univ. Ser. in Higher Math., Van Nostrand, Princeton, 1953. MR 14 837.

M. Kobayashi

On submanifolds in spaces of constant and constant holomorphic curvatures, Proc. Japan Acad. 44(1968), 334-339. MR 37 6878.

S. Kobayashi and K. Nomizu

[1] Foundations of Differential Geometry I, Interscience Tracts in Pure and Appi. Math. 15, Interscience Publishers (John Wiley and Sons, Inc.) New York, 1963. MR 27 2945.

[2] Foundations of Differential Geometry II, Interscience Tracts in Pure and Appl. Math. 15, Interscience Publishers (John Wiley and Sons, Inc.) New York, 1969. MR 38 6501.

H.B. Lawson, Jr.

Local rigidity theorems for minimal hypersurfaces, Ann. of Math. (2) 89(1969), 187-197. MR 38 6505.

J.D. Moore

[1] Isometric immersions of space forms, Notices of the A.M.S. 17 (1970), 452.

[2] Isometric immersions of space forms in space forms of larger curvature, to appear.

J.R. Munkres

Elementary Differential Topology, rev. ed., Ann. of Math. Studies 54, Princeton Univ. Press, Princeton, 1966. MR 29 623 and MR 33 6637.

J. Nash

[1] C¹ isometric imbedding, Ann. of Math. (2) 60(1954), 383-396. MR 16 515.

[2] The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63(1956), 20-63. MR 17 782.

M. Okumura

On contact metric immersion, Kodai Math. Sem. Rep. 20 (1968), 389-409

T. Otsuki

A theory of Riemannian submanifolds, Kodai Math. Sem. Rep. 30 (1968) 282-295. MR 38 2707.

J.J. Stoker

Differential Geometry, Pure and Appi. Math. XX, Wiley-Interscjence (John Wiley and Sons, Inc.), New York, 1969.

D.J. Struik

Lectures in Classical Differential Geometry, 2d ed., Addison-Wesley Ser. in Math., Addison-Wesley, Reading, 1961. MR 12 127.

R.H. Szczarba

[1] On existence and rigidity of isometric immersions, Bull. Amer. Math. Soc. 75(1969), 783-787.

[2] Addendum to: On existence and rigidity of isometric immersions, Bull. Amer. Math. Soc. 76(1970), 425.

H. Whitney

Differential Manifolds, Ann. of Math (2) 37 (1936), 645-680. FM 62 1454 (footnote 2).

T. J. Wilimore

An Introduction to Differential Geometry, corrected ed., Clarendon, Oxford, 1964. MR 28 2482.

J.A. Wolf

Spaces of Constant Curvature, McGraw-Hill Ser. in Higher Math., McGraw-Hill, New York, 1967. MR 36 829.

Y. -C. Wong

A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math. 67(1963), 363-365. MR 27 5173.

Y. -C. Wong and H. -F. Lai

A critical examination of the theory of curves in three dimensional differential geometry, Tohoku Math. J. (2) 19 (1967), 1-3 1. MR 35 4825.

¹ "MR"

Mathematical Reviews, American Mathematical Society.

² "FM"

Jahrbuch uber die Fortschritte der Mathematik, Preussischen Akademie der Wissenshaften.

³ (added in the year 2001)

Through the late 1930's, "FM"² took responsibility for publishing abstracts for all mathematics papers which appeared in a broad selection of mathematics journals. "Math Reviews"¹ was founded to fill the void left when "FM" ceased publication. For whatever reason, an abstract for "Fialkow" [1938] appears in neither publication.

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