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I have a problem with the sentence

Disappointed, they turned back, leaving a number of oxygen bottles behind.

The form of 'leave' here is 'leaving.' I can see this in other sentences like:

She hurried out the door, taking her coat with her.
They left early, bringing all the equipment they were likely to need.

I have been through a few grammar books trying to get an explanation why this is a gerund. If anyone could help, I'd appreciate it.

TF.
Comments  
I think 'turned' and 'leaving' occurred simultaneously.
TobiasI have a problem with the sentence

Disappointed past participle (adjective describing their state), they turned back, leaving present participle (accompanying action) a number of oxygen bottles behind.

The form of 'leave' here is 'leaving.' I can see this in other sentences like:

She hurried out the door, taking her coat with her.
They left early, bringing all the equipment they were likely to need.

I have been through a few grammar books trying to get an explanation why this is a gerund. If anyone could help, I'd appreciate it.

TF.

I hope my explanation above helps.
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trying to get an explanation why this is a gerund
I can see why you're having trouble. These -ing words are participles (verbal adjectives), not gerunds (verbal nouns).

It's hard to know whether your problem consists merely of finding the proper terminology or of understanding the meaning(s) of the sentence(s).

CJ
I am trying to find out the terminolgy of the '-ing' form of the words, and the reason why they need to be used there. I'm quite clear about the meaning of the sentence.
Thanks Phillip. It's a present participle, accompanying action, not a gerund. Thanks also to CalfJim - I was looking for the terminology, not the meaning of the sentence.
TF.
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My partner writes -ing ending words in the middle of sentences like the following examples I posted below and it drives me crazy. Can you please explain if these sentences are correct or not.

Sentence 1: I always uphold my professional merit suggesting I provide my current agency a two weeks resignation notice.

Sentence 2: Given that I speak only Spanish to my current patients suggesting my experience and fluency with this language, and that I am adhering to the lower end of the salary range, I am expecting a high meeting point of ten percent pay differential for my salary.