TOTALLY REDUCIBLE FOCAL SET WITH STEREOGRAPHIC PROJECTION

Research Article

Year 2004, Issue: 006, 231 - 238, 15.10.2004

In [1], Carter and the author introduced the idea of an immersion f :M→Rn with

totally reducible focal set (TRFS). Such an immersion has the property that, for

all p∈M , the focal set with base p is a union of hyperplanes in the normal plane to

f (M) at f (p) . In this study, we show that the property of an immersion having

TRFS is preserved under inverse image of stereographic projection.

[1] S. Carter and R. Ezentas, Immersion with totally reducible focal set, Journal of Geometry, 45 (1992), 1-7.
[2] A.M. Flegmann, Parallel rank of a submanifold of Euclidean space, Math. Proc. Camb. Phil. Soc., 106 (1989), 89-93.
[3] J. Milnor, Morse Theory, Princeton Univ. Press, Princeton, 1963.
[4] R.S. Palais and C.L. Terng, Critical point theory and submanifolds geometry, Lecturer Notes in Maths. 1353, Springer-Verlag, Berlin, 1988.
[5] C.L. Terng, Submanifolds with flat normal bundle, Math. Ann, 277 (1987), 95-111.

Year 2004, Issue: 006, 231 - 238, 15.10.2004

S. Carter ve yazar, f :M→Rn tamamen indirgenebilen focal cümleye (TRFS)

sahib immersiyon tanımını [1] de verdi. Bu immersiyon her p∈M için, p ye bağlı

focal cümle, f (p) de f (M) ye normal düzlemdeki hiperyüzeylerin bir

birleşimidir. Bu çalışmada bu özelliği sağlayan TRFS ye sahip immersiyonlar,

stereografik projeksiyonun ters görüntüsü altında korunduğu gösterildi.

[1] S. Carter and R. Ezentas, Immersion with totally reducible focal set, Journal of Geometry, 45 (1992), 1-7.
[2] A.M. Flegmann, Parallel rank of a submanifold of Euclidean space, Math. Proc. Camb. Phil. Soc., 106 (1989), 89-93.
[3] J. Milnor, Morse Theory, Princeton Univ. Press, Princeton, 1963.
[4] R.S. Palais and C.L. Terng, Critical point theory and submanifolds geometry, Lecturer Notes in Maths. 1353, Springer-Verlag, Berlin, 1988.
[5] C.L. Terng, Submanifolds with flat normal bundle, Math. Ann, 277 (1987), 95-111.

There are 5 citations in total.

APA	Ezentaş, R. (2004). TOTALLY REDUCIBLE FOCAL SET WITH STEREOGRAPHIC PROJECTION. Journal of Science and Technology of Dumlupınar University(006), 231-238.

HAZİRAN 2020'den itibaren Journal of Scientific Reports-A adı altında ingilizce olarak yayın hayatına devam edecektir.