Nash C1-embedding theorem for Carnot-Caratheodory metrics

Differential Geometry and its Applications North-Holland

I97

6 (1996) 197

Erratum

Nash C l-embedding theorem for Carnot-Caratheodory metrics Dif. Geom. Appl. 5 (1995) 105-119

Giuseppina

D’Ambra’

Dipartimento di Matematica,

UniversitLi di Cagliari, 09124 Cagliari, Ita!\

Corrige

Errata ---p. 107: statement of Theorem 0.4.A. dimW ;> 2dimV+3 .._P.

12: statement of Theorem 2.1. dimW ;> 2dimV+3

---p.

dim W 3 max(2 dim V + 3. 3 dim V - 2)

14: 4th row Hermitian of dimension m

---p.

dimW>max(2dimV+3.3dimV-2)

Hermitian of dimension 2n

14: 5th row 2m

m

---p. 1 14: statement of Proposition 2.2.B If rank T > 2 rank S

If rank T 3 3 rank S

.--p. 115: Remarks 2.3.A’(ii) so we do not loose . . . for our proof.

delete

.- p. 115: Remarks 2.3.A’(ii) change the last four rows as follows: . as a minimum and since we use normal extension we need extra 4 dimension i.e., dim W > 2 dim V + 3 (where dim W is even as we assume that W is quasi-Hermitian). But, since we use a transversality argument (see 2.1.F) we have an extra limitation, namely we need dim W 2 max(2dim V + 3.3dim V - 2).

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