Errata on a paper entitled ‘Almost K¨ ahler structures with a fixed K¨ ahler class’ this journal vol. 27 (2004)

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Toyama Math. J.

Vol. 33(2010), 55-56

Errata on a paper entitled ‘Almost K¨ ahler structures with a fixed K¨ ahler class’ this journal vol. 27 (2004)

Takashi Koda

Abstract. In this article, we correct errata of the preceding paper entitled “Almost K¨ahler structures with a fixed K¨ahler class”.

1. Corrections

p128 ↓ 3 line dA(JA, Y ) ⇒ dA(JX, Y ) p128 ↑ 5 line −ρ

^∗ad

is removed

p129 ↓ 9 line −ρ

^∗

is removed p129 ↓ 14 line −ρ

^∗

is removed p129 ↑ 7 line

Z

M

{T

_ij

h

^ij

+ S

_i

A

ⁱ

} dv

_g

⇒

Z

M

{T

_ij

h

^ij

+ S

_i

A

ⁱ

} dv

_g

= 0 p130 ↑ 10 line 3ρ

^∗

(X, Y ) is removed

p130 ↑ 9 line 3ρ

^∗

(Y, X ) is removed p131 ↓ 6 line (6) ⇒ (7)

p131 ↓ 7 line 3ρ

^∗

(X, Y ) is removed 2. Remark

In the proof of Proposition 2, we should consider the symmetric part of

∗-Ricci tensor ρ

^∗

, which is given by 1

2 (ρ

^∗

(X, Y ) + ρ

^∗

(Y, X )).

2000Mathematics Subject Classification. Primary 53C15 ; Secondary 58E11 . Key words and phrases. almost K¨ahler structure.

55

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56

TakashiKoda

In general, we know

ρ

^∗

(JX, JY ) = ρ

^∗

(Y, X ).

Hence the symmetric part of ρ

^∗

may be written as 1

2 (ρ

^∗

(X, Y ) + ρ

^∗

(JX, JY )), which is J-invariant. So is the symmetric part of ρ

^∗

◦ J .

References

[1] T. Koda, Critical almost Hermitian structures, Indian J. Pure Appl.

Math., 26(1995), 679–690.

[2] T. Koda, Almost K¨ahler structures with a fixed K¨ahler class, Mathe- matical Journal of Toyama Univ., 27(2004), 125–131.

TakashiKoda

Department of Mathematics Faculty of Science

University of Toyama

Gofuku, Toyama 930-8555, JAPAN e-mail: [email protected]

(Received October 7, 2010)