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Post Closed as "Needs details or clarity" by Michael Seifert, Miyase, Cosmas Zachos
Replaced "Hamilton" with "del" to avoid confusion
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A.V.S.
A.V.S.
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Hamilton Del operator confusion

The very first thing my textbook says is that the HamiltonDel operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this?

Hamilton operator confusion

The very first thing my textbook says is that the Hamilton operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this?

Del operator confusion

The very first thing my textbook says is that the Del operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this?

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Krum Kutsarov
Krum Kutsarov
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Hamilton operator confusion

The very first thing my textbook says is that the Hamilton operator is defined as: $$\vec{\nabla}=\vec{a}^i\nabla_i$$ Where $\nabla_i$ is the covariant derivative and " $\vec{a}^i$ is the curvilinear basis of the curvilinear coordinates $\xi ^i$". However I can't understand if that should be the dual basis (because of the upper index) or it is just written that way to obey einstein notation (upper and lower repeating) or maybe it is a mistake (I don't believe it to be). Can you help me clarify this?